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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  sml512.bt              GAP library of groups           Hans Ulrich Besche
##                                               Bettina Eick, Eamonn O'Brien
##

SMALL_GROUP_LIB[ 512 ][ 72 ] := [
"%%%%%k&8(/%,%%DEG)%)%dzjdvC,,8 2t88YeSTUVWX6789:<=>ABCDEFGHYZ[]^abcdefghijk\
!2eA8Ye%*!&bVA8e-r!&bWA8e-r!&bXA)e+z!&u8V9k*t!&u8Y9k*t &cV]&n%I6Y.QAd(K0S*M:\
^2UEh,O4W!&bVB8e%-!&bVB<e%-!&f8]9k%-!&u8W9k%(!&x8W9k%(!&cDW9n&Y!EbVA8e-r!EbW\
A8e-r!EbXA)e+z!EbVB8e%- EbVB<e%&()./016789ABCDIJKLQRSTYZ[]defg*+,-2345:<=>EF\
GHMNOPUVWX^a",
"%%%%%k98b/%),%DEG)%)%dzddtC,,8 D/2=m/6AIQYd &85Ad/%6.QAd(0S&J*M:^2UEh+3V-5X\
 &80<d/%I6Y.Ad*M &85Am/%.&7)9*2U,4W+<3F &%0<m/%I.A!&859v/(P!*85Ad/-l!*86<d/.\
=!*85=d/.> *87,m/%I(8&J)L9]*M:^,O=b+N<a-P>c2U4G3V5XHk *85=m/%I6Y*M:^(K0S,O=b\
4WGj!*859v/(P!H85Ad/-l!H86<d/.=!H85=d/.> H87,m/%I(8&J)9*M:^,O=b+N<a-P>c2U4G3\
V5H H85=m/%I6Y*M:^(K0S,=4G!H859v/(P!385Ad/-l!386<d/.=!385=d/.> 387,m/%I(8&J7\
Z)L*M:^,O=b+N<a-P>c2U4G3VFi5X 385=m/%I6Y*M:^(K8[0SCf,O4W!3859v/(P!Q85Ad/-l!Q\
86<d/.=!Q85=d/.> Q87,m/%I(8&7)L*M:^,O=b+N<a-P>c2U4G3F5X Q85=m/%I6Y*M:^(80C,O\
4W!Q859v/(P!%]JVgD*t!%]JYgD*t!%WJ]gD%-!%]JWgD%( %WJWgD%(*,.02468:=ACEGIKMOQS\
UW",
"%%%%%k98b/%),%bFG<%)%d}djzCh,: %Px,JJK%QRSTUVWX6789:<=>ABCDEFGHYZ[]^abcdefg\
hijk!)&bJ.,,D-r!)&bK.,,D-r!)&bL.&,D+z!)&bJ.J,D%-!)&bJ.K,D%-!G&bJ.,,D-r!G&bK.\
,,D-r!G&bL.&,D+z!G&bJ.J,D%-!G&bJ.K,D%-!&&bJ.,,D-l!&&bK-,,D.=!&&bJ-J,D.> &&bJ\
.-,D%I(K&7/B)1*M2U,O4W+<3F->5H &&bK--,D%I*M(80C,4 &&bJ-K,D%I6Y*M:^(80C,O4W &\
&bJ,L,D%6*:&7/B+3IYM^JZReNV(80C,4)9->K[SfOWL]Pc E&t,J,-%%I*(K0S,4&J6Y:8C=G7Z\
 E&b,K,-%%I6Y*M:^(0,O4W E&b,LJ-%%I6Y(K8[&/)L1T*M2,O=b4G+N E&k,KJ-%%I.*:2E(K \
E&b,JK-%%I6Y.A*M:^2E(K8[0SCf E&h5M/6M%I*MU6Y E&bDJj-D%6:^&J.Q/B3Fi0CGj1T E&b\
,J--%%(,IKO68=Y[b.024ACEG!0&bJ.,,D-l!0&bK-,,D.=!0&bJ-J,D.>!0&bJ%-%D-6",
"%%%%%k98b/%)%%bDG2%)%d,ddtA,,8 09die8[&J/R)1*M:^2UEh,O=b4WGj+N3V-P5X 09mKe%\
I6Y*M:^(K0S,4 09dTe%I6Y*M:^(K0S,=4G 09d7e%6*:&7/B+3IYM^JZReNV(80C,4)9->K[SfO\
WL]Pc!N9dhe-l!N9mJe.=!N9dSe.> N9die%6(8&J/R)L1T*:2E,=4G+N3V-P5X N9mKe%6*:(K0\
S,O4W N9dTe%I6Y*M:^(K0S,O=b4WGj N9d7e%6*:&7/B+3IYM^JZReNV(80C,4)9->K[SfOWL]P\
c!)Wdhe-r!)Wmhe-r!)Wvce+z!)Wdqe%-!)Wdre%-!GWdhe-r!GWmhe-r!GWvce+z!GWdqe%-!GW\
dre%- EWdhe%6.QAd(0S&J*M:^2UEh+3V-5X EW1Je%I6Y.QA*M EWdie%I&7/B)1T*2U,4W+N<a\
3VFi EW1Ke%I*:2Eh E]g,k%I*(K0S,4&J6Y:8C=G7Z EVgJk%I6Y*M:^(0,O4W EVgqk%I6Y(K8\
[&/)L1T*2U,=4WGj+N EYgSk%.Q*:2E(K EVg6k%6.QAd*:2UEh(K",
"%%%%%k9%D/8,,%DDG2%)%d,ddtA,,8!E8g0M9E E9+Cn%6*:^&J.Q/B3VF(K)9]->0SC4G1T!E9\
d5e(] E8g-k%(,IKO68=Y[b.024ACEG!E&d6e&Y!09dhe-l!09mJe.=!09dSe.> 09die%I6Y(K8\
[&/)L1T*M:^2UEh,O=b4WGj+N3V-P5X 09mKe%I6Y*M:^(0,O4W 09dTe%I6Y*M:^(K0S,O=b4WG\
j!09d7e(P!N9dhe-l!N9mJe.=!N9dSe.> N9die%6(8&/)1*:2E,=4G+N3V-P5X N&v^e6Y8[7B9\
D* N9dTeI6Y*M:^(K0S,=4G!N9d7e(P HAg,k%I.Q*2(K0S,4&J+N6YAd:E8[Cf=G7Z<a H8gJk%\
I6Y.QAd*M:^2UEh(K0S,O4W H8gqk%I.Q(K0S&7/B)91D*2U,4W+<3F H<gSk%.Q*2U(80C H8gK\
k%I6Y.A*M:^2E(K8[0SCf H8gBk*M2U,O4W+N<a3VFi%&)IJL679YZ] H8f{k235UVXEFHhik%&(\
)6789!H%eTk(3!D]g,k*t!D]gJk*t!D]gkk*j!DVgik%-!DVgrk%-!G]g,k*t!G]gJk*t!GVg/k.\
Z",
"%%%%%k&8b/8,,%bFG<,)%d,ddtA,,8 H2L9w<3V6YAd:^Eh7ZBe<aFi(K0S,O4W)L1T-P5X8[Cf\
=bGj9]Dg>cHk!H2J9vY%-!H2J9yY%-!/HJVv9-r!/HJYv9-r!/HJ]tW+z!/HJVy9%-!/HJVyW%-!\
MHJVv9-r!MHJYv9-r!MHJ]tW+z!MHJVy9%-!MHJVyW%- GHL9d<%I*(K0S,4&J6Y:8C=G7Z GHJ9\
m<%I6Y*M:^(0,O4W GHJ9y<%I6Y(K8[&/)L1T*2U,O4W+N GHK&p<%I6.A*M GHJ9gY%I.Q*M2U(\
K8[0SCf GHJEjx%6:^&J.Q/B3Fi0CGj1T GHJ9dY%(,IKO68=Y[b.024ACEG )D5Vv9%6.QAd(80\
SCf&J/R*M:^2UEh+3V-5X )D5Yv9%I6Y.QAd&J/)L1*M2U,O4W+N3V )D5VvW%I.Q&7/B)91D*2U\
,4W+<3F )D5YvW%.Q(0S&7/B*M2U+3-5 )D5Vg9%(*,.02468:=ACEGIKMOQSUWY[^bdfh",
"%%%%%k9%D/8)%%%DG)))%d,ddtA,,8 (59zDi(),-014589=>CDGHKLOPSTWX[]bcfgjk!FhVi%\
*t!FhYi%*t!FhWi%*t!FhZi%*t F/X{D%I6Y:^&J7Z<a.QAd2UEh/RBe3VFi0SCfGj1TDgHk!F,]\
r%%-!F,^r%%- 15AhD%6.QAd(K0S&J/R*M:^2UEh,O=b4WGj+N3V-P5X 16<hD%6.QAd*M2U(K0S\
 15AqD%I.Q(80SCf&J/R*M:^2UEh,O=b4WGj+N3V-P5X 16<qD%I.Q*:2UEh(K0S!159zD%P!O5A\
hD-r!O6AhD-r O5AqD%6.A(80C&J/R)L1T*:2E,=4G+N3V-P5X O6AqD%6.A(80C&J/R)L1T*:2E\
,=4G+N3V-P5X!O5BhD%-!O5BqD%- IhVi%%I*M(K0S,O4W&J)L6Y:^8C=G7Z9] IhYi%%I.Q(K0S\
&+)L-P6YAd8[Cf7Z<a9> IhWi%%I(K&+)1-56Y8[7<9D>H IhZi%%I*M(K,O&/)16:8=7B9D I,X\
r%%&()./016789ABCDIJKLQRSTYZ[]defg*+,-2345:<=>EFGHMNOPUVW",
"%%%%%ku8d/8,%%(bY,,,%dhjdvA,,8 DH0P,5KkEIMQUY^dh DQ0U,5,k%I*M(K0S,4&J+N6Y:^\
8C=bGj7Z<a DQ0S,6,k%I6Y.QAd*M:^2UEh(K0S,O4W DQ0S,7Jk%I.Q(K0S&J7Z/RBe)L9]1TDg\
*M2U+N3V->5XHk DQ0T,6Jk%I.Q(K0S,O=b4G!DQ0S,5ik%- /%G,q,5e%&IJ./*+MN23()KL01S\
T67YZAB:<^aEF89[]CDfg /%G,q,6e%&IJ./*+MN23()KL01ST67YZAB:<^aEF89[]CDfg /%G,r\
,5e%&./QR*+23UV()KL01ST67ABde:<EFhi89[]CDfg /%G,r,6e%&./QR*+23UV()KL01ST67AB\
de:<EFhi89[]CDfg!/%G,5J7e%P!/%G,6J7e%P P%G.5,5e%I.*M2(0S,4W6Ad:Eh8[C=bG7ZBe<\
aFi P%G,r,5e%.Q*2U(K0S,O4W&J/+N36YA:^E8Cf=Gj P%G.5,6e%I.Q*M2U&/R+3V)L1-P56Ad\
:Eh7ZB<aF P%G-r,6e%I.*M2(K0S,O4W&/R+3V6Ad:Eh7ZB<aF!0%G,5,7e%P!0%G,5,Ue%P!0%G\
,5J7e%P!0%G,5JUe%P!0%G,6,7e%P!0%G,6,Ue%P 0%G,6J5e%(*,.02468:=ACEGIKMOQSU",
"%%%%%kW8b/%%%%&%P%%%%dej(9A,%/ )dSzVYZ^adehi(),-014589=>CDGHKLOPSTWX[]bcfgj\
k!)dTz%P 2thh%*(,)-IMKOLPAECGDHdhfjgk 2whh6:8=9>Y^[b]c.20415QUSWTX 2thq6:8=7\
<Y^[bZa.204/3QUSWRV 2whq%*(,&+IMKOJNAECGBFdhfjei 2Bhh%&()*+,-QRSTUVWXYZ[]^ab\
cABCDEFGH 2BhqIJKLMNOP./0123456789:<=>defghijk!2m,h&1!2dJh&1!2d,q&1!2mJq&1 P\
thh%*(,)-IMKOLPAECGDHdhfjgk Pwhh6:8=9>Y^[b]c.20415QUSWTX Pthq6:8=7<Y^[bZa.20\
4/3QUSWRV Pwhq%*(,&+IMKOJNAECGBFdhfjei PBhh%&()*+,-QRSTUVWXYZ[]^abcABCDEFGH \
PBhqIJKLMNOP./0123456789:<=>defghijk!Pm,h&1!PdJh&1!Pd,q&1!PmJq&1!&d,z%P!&d-z\
%P!&d5z%P!&d6z%P &dJz%&*+./2367:<ABEFIJMNQRUVYZ^adehi(),-014589=>CDGHKLOPSTW\
X[]bcfgj",
"%%%%%kW%D/%%%%&%P%%%%b)j(9A,%/ *GPA!.Kz%P!.Sz%P!.Tz%P!L,z%P!L-z%P!L5z%P!L6z\
%P!LJz%P!LKz%P!LSz%P!LTz%P!7,z%P!7-z%P!75z%P!76z%P 7Jz%&*+./2367:<ABEFIJMNQR\
UVYZ^adehi(),-014",
"%%%%%kW8D/%%%%&%P%%%%b)j(9A,%/ 1m>468:=ACEGIKMOQSUWY[^bdfhj!1ma%P!1pC%P!1pa\
%P!OdC%P!Oda%P!OgC%P!Oga%P!OmC%P!Oma%P!OpC%P!Opa%P!+dC%P!+da%P!+gC%P!+ga%P )\
m:%*.26:AEIMQUY^d",
"%%%%%kW/D/%%%%&%P%%%%b)j(9A,%/ .JzFIJMNQRUVYZ^adehi(),-014589=>CDGHKLOPSTWX\
[]bcfgjk!.Kz%P!.Sz%P!.Tz%P!L,z%P!L-z%P!L5z%P!L6z%P!LJz%P!LKz%P!LSz%P!LTz%P!7\
,z%P!7-z%P!75z%P 76z%&*+./2367:<ABEFIJMNQRUVYZ^adehi(),-014589=>CDGHKLOPSTW",
"%%%%%kW8J/%%%%&%P%%%%b)j(9A,%/ 2WrbEIMQUY^dh!2wjb%P!2wsb%P!2xjb%P!2xsb%P!Pt\
jb%P!Ptsb%P!Pujb%P!Pusb%P!Pwjb%P!Pwsb%P!Pxjb%P!Pxsb%P!&tjb%P!&tsb%P!&ujb%P &\
uqb%(*,.02468:=ACEGIKMOQSUWY[^bdfh",
"%%%%%kW8G/%%%%&%P%%%%dej(9A,%/ (,[ti(),-014589=>CDGHKLOPSTWX[]bcfgjk!(-:t%P\
!(->t%P!(-Xt%P!(-[t%P 1d:8%*(,)-IMKOLPAECGDHdhfjgk 1m:86:8=9>Y^[b]c.20415QUS\
WTX 1d:V6:8=7<Y^[bZa.204/3QUSWRV 1m:V%*(,&+IMKOJNAECGBFdhfjei /y:8%&()*+,-QR\
STUVWXYZ[]^abcABCDEFGH /y:VIJKLMNOP./0123456789:<=>defghijk!1J:8&1!1-:8&1!1,\
:V&1!1K:V&1 Od:8%*(,)-IMKOLPAECGDHdhfjgk Om:86:8=9>Y^[b]c.20415QUSWTX Od:V6:\
8=7<Y^[bZa.204/3QUSWRV Om:V%*(,&+IMKOJNAECGBFdhfjei My:8%&()*+,-QRSTUVWXYZ[]\
^abcABCDEFGH My:VIJKLMNOP./0123456789:<=>defghijk!OJ:8&1!O-:8&1!O,:V&1!OK:V&\
1!+,:t%P!+,>t%P )%X8%.6AIQY",
"%%%%%kW8h/%,%%&%P%%%%dej(vA,%/!*J9cz8n!*J9fz%P!*J<cz%P!*J<fz%P!*J=cz%P!*J=f\
z%P 3L,ch%*(,)-IMKOLPAECGDHdhfjgk 3LJch6:8=9>Y^[b]c.20415QUSWTX 3L,cq6:8=7<Y\
^[bZa.204/3QUSWRV 3LJcq%*(,&+IMKOJNAECGBFdhfjei 3Fqch%&()*+,-QRSTUVWXYZ[]^ab\
cABCDEFGH 3FqcqIJKLMNOP./0123456789:<=>defghijk!3K8ch&1!3J<ch&1!3J8cq&1!3K<c\
q&1 QL,ch%*(,)-IMKOLPAECGDHdhfjgk QLJch6:8=9>Y^[b]c.20415QUSWTX QL,cq6:8=7<Y\
^[bZa.204/3QUSWRV QLJcq%*(,&+IMKOJNAECGBFdhfjei QFqch%&()*+,-QRSTUVWXYZ[]^ab\
cABCDEFGH QFqcqIJKLMNOP./0123456789:<=>defghijk!QK8ch&1!QJ<ch&1!QJ8cq&1!QK<c\
q&1 %5:bh%6Y*M:(K8[,O=b)L9->c.QAd0SCf4WGj1TDg!%58nb.B",
"%%%%%kW8b/%)%%&%P%%%%b)d(tA,%/ %}Sb,=b&7Z+N<.QAd2UEh0SCf/RBe %}Kb%6Y*M:(K8[\
,O=b)L9->c.QAd0SCf4WGj1TDg %}6b%I6Y*M:^(K8,=b&7Z+N<.QAd2UEh0SCf/RBe!%}Jb%*!%\
}-b%* /j,b%.*2,4IQMUOW6:E=Y^hb /jSb%.*2,4IQMUOW6:E=Y^hb /jKb%.*2,4IQMUOW6:E=\
Y^hb /j6b%.*2,4IQMUOW6:E=Y^hb /7zb%&()6789IJKLYZ[]2345EFGHUVWXhijk /7{b./01A\
BCDQRSTdefg*+,-:<=>MNOP^abc!/}Jb%*!/}-b%* )vhb%6.QA(80SCf&J7/B*M:^2UEh+N<a3V\
Fi )yhb%I.Q(K)L*M:^2UEh+N<a3VFi )}5%%I6*M:(8[,O=.QAd0SCf )vib%I6Y.QAd&J7Z/RB\
e*:2UE,=4WGj+N<3F )yib%I6Y.QAd&J7Z/RBe*M2U,O-P )}T%%I6*M:(8[,O=.QAd0SCf Pvhb\
%6.QA(80Cf*M:^+N<a Pyhb%I)L*:^2UE+<a3Fi Pvib%I6Y&J7Z*:2UE-P>5H Pyib%I6.QA&7Z\
/RB*M,O!&v.b%P!&v7b%P!&y.b%P!&y7b%P &vJb%(*,.02468:=ACEGIKMOQSUWY[^",
"%%%%%/W8D/%)%%&%P%%%%b)d(tA,%/ .<zadehi(),-014589=>CDGHKLOPSTWX[]bcfgjk!.=z\
%P!.Yz%P!.Zz%P!L8z%P!L9z%P!LVz%P!LWz%P!L<z%P!L=z%P!LYz%P!LZz%P 7Ah%6.QAd(80S\
Cf&J7Z/B)L9]1D*M:^2UEh+N<a3VFi 7]h%I.Q(K0S&J/R)L1T*M:^2UEh+N<a3VFi!7{b+z 7Aq\
%I6Y.QAd&J7Z/RBe*:2UEh,=4WGj+N<a3F-P>c5H 7]q%I6Y.QAd&J7Z/RBe*M2U,O4W+N3V-P5X\
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"%%%%%kW8J/%)%%&%P%%%%b)d(tA,%/!)yT%=a Gvhb%6.QAd(80SCf&J7Z/B)L9]1D*M:^2UEh+\
N<a3VFi Gyhb%I.Q(K0S&J/R)L1T*M:^2UEh+N<a3VFi!G}q%+z Gvib%I6Y.QAd&J7Z/RBe*:2U\
Eh,=4WGj+N<a3F-P>c5H Gyib%I6Y.QAd&J7Z/RBe*M2U,O4W+N3V-P5X!G}r%+z 2vhb%6.QAd(\
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z 2vib%I6Y.QAd&J7Z/RBe*:2UEh,=4WGj+N<a3F-P>c5H 2yib%I6Y.QAd&J7Z/RBe*M2U,O4W+\
N3V-P5X!2}r%+z Pvhb%6.QAd(80SCf&J7Z/B)L9]1D*M:^2UEh+N<a3VFi Pyhb%I.Q(K0S&J/R\
)L1T*M:^2UEh+N<a3VFi!P}q%+z Pvib%I6Y.QAd&J7Z/RBe*:2UEh,=4WGj+N<a3F-P>c5H Pyi\
b%I6Y.QAd&J7Z/RBe*M2U,O4W+N3V-P5X!P}r%+z &vhb%6.QAd(80SCf&J7Z/B)L9]1D*M:^2UE\
h+N<a3VFi &yhb%I.Q(K0S&J/R)L1T*M:^2UEh+N<a3VFi!&}q%+z &vib%I6Y.QAd&J7Z/RBe*:\
2UEh,=4WGj+N<a3F-",
"%%%%%kW8J/%,,%&%P8%%%b)dv}ACh8 &Fbk2DDI6Y.A &Fkt<bD%I6Y.QAd&J7Z/RBe*M2U,O4W\
+N3V-P5X!&Ftw<%D+z 0Fbt8bD%6.QA(80SCf)L91D*M:^2UEh+N<a3VFi 0Fkt8bD%I(K0S)L*M\
:^2UEh+N<a3VFi 0Ftn8%D%I6*M:(K8,=b.QAd0SCf 0Fbt<bD%I6Y.QAd&J7Z/RBe*:2UE,=4WG\
j-P>5H 0Fkt<bD%I6Y.QAd&J7Z/RBe*M,O4W-P 0Fte<%D%I6*M:(K8,=b.QAd0SCf NFbt8bD%6\
.QA(80SCf)L91D*M:^2UEh+N<a3VFi NFkt8bD%I(K0S)L*M:^2UEh+N<a3VFi NFtn8%D%I6*M:\
(K8,=b.QAd0SCf NFbt<bD%I6Y.QAd&J7Z/RBe*:2UE,=4WGj-P>5H NFkt<bD%I6Y.QAd&J7Z/R\
Be*M,O4W-P NFte<%D%I6*M:(K8,=b.QAd0SCf *Ftb8bD%6Y*M:(K8[,O=b)L9->c.QAd0SCf4W\
Gj1TDg *Ftn8bD%I6Y*M:^(K8,=b&7Z+N<.QAd2UEh0SCf/RBe *Ftk<bD%6Y*M:(K8[,O=b)L9-\
>c.QAd0SCf4WGj1TDg *Fte<bD%I6Y*M:^(K8,=b&7Z+N<.QAd2UEh0SCf/RBe!*Ftk8bD%*!*Ft\
b<bD%* 3F8b8bD%.*2,4IQMUOW6:E=Y^hb 3F8n8bD%.*2,4IQMUOW6:E=Y^hb 3F8k<bD%.*2,4\
IQMUOW6:E=Y^hb 3F8e<bD%.*2,4IQMUOW6:E=Y^hb 3DVz8bD%&()6789IJKLYZ[]2345EFGHUV\
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