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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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#############################################################################
##
#W  col21.z                GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 846 ] :=
[ 1650448112516963, 87381753695935, 1609851610153584635, 2301416571,
103303867039, 2435740251, 87381816380319, 1946511406883, 73925158322592799,
2207 ]; 

PROPERTIES_SMALL_GROUPS[ 846 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 848 ] :=
[ 193966864211475590556723, 4490077591696854976, 164392496343299995353230387,
228734508176914954291, 193966583583189437642803, 164483900012044176116447283,
164483900012374327048042547, 139482347210493700878079487027,
228734508176534750259, 193966583583189057438771, 228734508175774342195,
193966863221027358219315, 193966583583188297030707, 228734508181477402675,
170918500914674820997287987, 144938888775644437950704583731,
144938888775644437951084787763, 122908177681746483571620838763571,
228734508181097198643, 5294874571994800, 10571065537515184,
8969546746067007152, 5294876853218992, 4484782722821025456,
3803095747349172583088, 3225025193565108187655856,
2734821364143024431316752048, 164392496062672871484042291,
139404836660865924815580785715, 193859075876582300474419,
164392496062672876046490675, 193859075876583060882483,
164392496062672876806898739, 193859075876587623330867,
193966583253044209108019, 269733361300262963, 228734178037389479987,
228734178036629071923, 280285828397006899, 201554835653904814794803,
201554835653894169081907, 170918500634706825681647667, 269733360159650867,
269733371945975859, 6229643066972, 6235346127452, 4484776491276805724,
5288651772467804, 228607403180981187635, 317741071990835, 51 ]; 

PROPERTIES_SMALL_GROUPS[ 848 ] := rec(
isNilpotent := [ 2, 20, -27, 45, -48, 51 ], 
isAbelian := [ 2, 20, 23, 45, 51 ], 
lgLength := rec( lgLength := [ 2, 3, 4, 5 ], pos := [ [ 50, -51 ], [ 11, -14,
19, -22, 30, -31, 34, -49 ], [ 4, -10, 15, -18, 23, -29, 32, -33 ], [ 1, -3 ]
] ),
frattFacs := rec( frattFacs := [ 5, 9, 14, 18, 22, 51, 55, 59 ], pos := [ 1,
2, 3, 19, 27, 34, 44, 48 ] ) );

SMALL_GROUP_LIB[ 850 ] :=
[ 73271172402995, 428391662399, 63645464485561331, 33686515, 505414463,
102761459, 429533430591, 86070267699, 365109301478207, 831 ]; 

PROPERTIES_SMALL_GROUPS[ 850 ] := rec(
isNilpotent := [ 4, 10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, 8, -10 ], [ 1, -4, 6, -7
] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 852 ] :=
[ 10511410268101, 723561542414969, 616476378679210139, 12317139730,
744485945280139, 20985509001100, 848993600139, 13061444831, 723561902560139,
139 ]; 

PROPERTIES_SMALL_GROUPS[ 852 ] := rec(
isNilpotent := [ 4, 10 ], 
isSupersolvable := [ 1, -5, 7, -10 ], 
isAbelian := [ 4, 10 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -10 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 855 ] :=
[ 276750440135, 53859799, 235884441421511, 325851731, 6227 ]; 

PROPERTIES_SMALL_GROUPS[ 855 ] := rec(
isNilpotent := [ 2, 5 ], 
isAbelian := [ 2, 5 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 4, -5 ], [ 1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5 ], pos := [ 1, 2 ] ) );

SMALL_GROUP_LIB[ 856 ] :=
[ 4979069256251427737, 55460740280276, 4262077366091789829145,
5816657819437193, 4979062340781383945, 5816657693189497, 5816658576923369,
64765079178, 65648813050, 47418587527220522, 6791116063337, 105 ]; 

PROPERTIES_SMALL_GROUPS[ 856 ] := rec(
isNilpotent := [ 2, 8, -10, 12 ], 
isAbelian := [ 2, 8, 12 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 11, -12 ], [ 3, -10 ], [
1, -2 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14 ], pos := [ 1, 2, 7, 10 ] ) );

SMALL_GROUP_LIB[ 858 ] :=
[ 18338586887, 19463639303, 15732906504455, 23888135, 117448967, 96215325,
101444825351, 11281813, 100340675879, 82100958789, 87040325302535, 263 ]; 

PROPERTIES_SMALL_GROUPS[ 858 ] := rec(
isNilpotent := [ 12 ], 
isAbelian := [ 12 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -12 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 860 ] :=
[ 4118494648215, 56244431081957, 48488297314447031, 1596307062,
3536345322694551, 130771483725551186615, 176813935216295, 65420296871,
4879141053, 56381491950503, 167 ]; 

PROPERTIES_SMALL_GROUPS[ 860 ] := rec(
isNilpotent := [ 4, 11 ], 
isAbelian := [ 4, 11 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 7, -11 ], [ 1, -6 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 868 ] :=
[ 1802814596105, 10452214894529, 9117226499850179, 415535370, 55808533440179,
12052800179, 2099520875, 10503652320179, 179 ]; 

PROPERTIES_SMALL_GROUPS[ 868 ] := rec(
isNilpotent := [ 4, 9 ], 
isAbelian := [ 4, 9 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 5, -9 ], [ 1, -4 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 870 ] :=
[ 8516674431, 963782151, 7419802694527, 334375973, 7401549871463,
822980149967, 6455248341908351, 895 ]; 

PROPERTIES_SMALL_GROUPS[ 870 ] := rec(
isNilpotent := [ 8 ], 
isAbelian := [ 8 ], 
lgLength := rec( lgLength := [ 4 ], pos := [ [ 1, -8 ] ] ),
frattFacs := rec( frattFacs := [ ], pos := [ ] ) );

SMALL_GROUP_LIB[ 872 ] :=
[ 5674008086110925675, 60880929865776, 4943650052089194640235,
4947728433773142571883, 6506877212951147, 5674000494446479979,
6506877076902251, 6506878029244523, 69793095204, 70745437476,
53026906800752676, 5671935336284229995, 7457656283243, 107 ]; 

PROPERTIES_SMALL_GROUPS[ 872 ] := rec(
isNilpotent := [ 2, 9, -11, 14 ], 
isAbelian := [ 2, 9, 14 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 13, -14 ], [ 4, -12 ], [
1, -3 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 11, 14, 17 ], pos := [ 1, 2, 3, 8, 11
] ) );

SMALL_GROUP_LIB[ 875 ] :=
[ 583933089, 665637, 674709, 2323108005, 779 ]; 

PROPERTIES_SMALL_GROUPS[ 875 ] := rec(
isAbelian := [ 1, -2, 5 ], 
lgLength := rec( lgLength := [ 2, 3, 4 ], pos := [ [ 5 ], [ 2, -4 ], [ 1 ]
] ),
frattFacs := rec( frattFacs := [ 4, 8 ], pos := [ 1, 4 ] ) );

SMALL_GROUP_LIB[ 876 ] :=
[ 74767299298731143, 85380632290439, 12095412350401, 856785854145671,
750546645986119823, 13786298424, 656779664946397193351, 85357386399887,
749978140956959879, 657181461934309183631, 880866522169487, 103195607183,
24149062733760, 76551177018880583, 977778376847, 14619382777, 856786257248399
, 143 ]; 

PROPERTIES_SMALL_GROUPS[ 876 ] := rec(
isNilpotent := [ 6, 18 ], 
isSupersolvable := [ 1, -12, 15, -18 ], 
isAbelian := [ 6, 18 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 8, 11, -18 ], [ 1, -7, 9,
-10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9, 11, 13 ], pos := [ 1, 2, 3, 4, 5
, 6 ] ) );

SMALL_GROUP_LIB[ 882 ] :=
[ 205778518662106412628191, 88504510097354975, 87909850624818355,
441134549129230559, 340557402179458763141591, 113260410839,
233308978074956987423, 88509897672687647, 68850131373023506843679,
100345254458399, 500152544508959, 112751782699, 441139936704563231,
99447314778547, 389085440577770974751, 127464479, 180819642699809473643608031
, 297889926540887, 103048211420639, 87913676259493343, 262936906934627807,
264324433788644831, 233134149023254791647, 231910350338011776479,
113268342359, 99901895507423, 101475055205855, 562735574615, 499484448458207,
99671032709107, 88903412323914235, 78420953241804388459, 127417963,
180408316527907868205241631, 694101194551583, 611999018009708831,
786731139359, 231911144109484250399, 205010932766217649961759, 113014518047,
116836079903, 99675372275999, 99896290799903, 101469450498335,
88108521545337119, 89496048399354143, 113268824471, 99671805020567,
103048211653919, 87913676259726623, 99901895740703, 101475055439135,
88108523328716063, 89496050182733087, 77711715997392098591,
78935514682635113759, 135364895, 113272307999, 115055935775, 638005535,
566303312159, 128397739, 562736056727, 499484448691487, 112752250099,
496334562039911, 440545300939307807, 287 ]; 

PROPERTIES_SMALL_GROUPS[ 882 ] := rec(
isNilpotent := [ 6, 16, 33, 68 ], 
isSupersolvable := [ 1, -16, 18, -33, 35, -37, 40, -68 ], 
isAbelian := [ 6, 16, 33, 68 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 35, -37, 39, 41, -46, 58
, -59, 61, 65, 67, -68 ], [ 7, 10, -11, 14, -17, 19, -24, 26, -27, 29, -30,
32, -34, 38, 40, 49, -57, 60, 62, 64, 66 ], [ 1, -6, 8, -9, 12, -13, 18, 25,
28, 31, 47, -48, 63 ] ] ),
frattFacs := rec( frattFacs := [ 5, 9, 13, 17, 21, 25, 30, 34, 38, 42, 46, 50
, 54, 58, 62, 66, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87,
91, 95 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 ] ) );

SMALL_GROUP_LIB[ 884 ] :=
[ 326721670923, 445504359183, 398873917980863, 33623024, 393676217977615,
288553537965835, 311696935710245322943, 311696937223013335231,
4334989536203440319, 347778818124087487, 5547325653183, 505413823, 371196155,
451209593023, 191 ]; 

PROPERTIES_SMALL_GROUPS[ 884 ] := rec(
isNilpotent := [ 4, 15 ], 
isAbelian := [ 4, 15 ], 
lgLength := rec( lgLength := [ 3, 4 ], pos := [ [ 11, -15 ], [ 1, -10 ] ] ),
frattFacs := rec( frattFacs := [ 3, 5, 7, 9 ], pos := [ 1, 2, 3, 4 ] ) );

SMALL_GROUP_LIB[ 888 ] :=
[ 17369860242693054524003, 19562449504942025315, 783838174717681345,
27374380019508308579, 24308482219835011034183, 881703810837360,
21577544378676433339804259, 15424435862936509393678643, 19560653599350934835,
17369860206224513010995, 19560653599290468659, 19560653600197461299,
24302948622639086168675, 21563675923583539961588807, 28935043375292172359,
28935043375231706183, 25694318592792042531911, 28935043376138698823,
25694318592792949524551, 25694318592792889058375, 22816554910474813635308615,
22029950642375987, 22029951488902451, 17371422592330582602035,
618785364810223995304896, 577915623497126302311595500,
24308416937135304356147, 30826929821535539, 27374343365214702899,
30826929761069363, 30826930668062003, 696045655821743086897, 882701805025585,
783835203468671281, 882701744559409, 882702651552049,
21585932113663865363180615, 27374416678276319303, 24308482109870679164999,
27374416678215853127, 27374416679122845767, 990738296316, 991645288956,
782073770611979772, 24299036463141355301171, 24308410852669627081799,
1234093640206127626481616, 1095875152622488315288037232, 22028224574914631,
57905970068716435043, 17400391832742262650467, 27368185806149429555,
24283418832875933770823, 32584423125418055, 25262284603463, 1762508731410288,
19595035916860438115, 34681463636039, 998417499373, 30826933570437191, 71 ];


PROPERTIES_SMALL_GROUPS[ 888 ] := rec(
isNilpotent := [ 6, 42, -44, 61 ], 
isSupersolvable := [ 1, -24, 27, -46, 49, 52, -55, 58, -61 ], 
isAbelian := [ 6, 42, 61 ], 
lgLength := rec( lgLength := [ 3, 4, 5 ], pos := [ [ 49, 54, -55, 58, -61 ],
[ 8, -12, 15, -48, 50, -53, 56, -57 ], [ 1, -7, 13, -14 ] ] ),
frattFacs := rec( frattFacs := [ 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 35, 38
, 41, 44, 47, 50, 53, 56 ], pos := [ 1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 21, 24,
25, 26, 31, 36, 41, 44 ] ) );