sml512.bm

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

SMALL_GROUP_LIB[ 512 ][ 65 ] := [
"%%%%%k%8b/8%%%%DM%%)%dAjdvA,,8 )lkchDI6Y.QAd*M:^2UEh(80C,=4G!)uwc,D*T!)ctcq\
D%*!)cwcqD%* GubchD%I.*M2(0S,4W&/+36Ad:Eh8[C=bG7B<F!GckchD.t Guwc,D%I.Q(K0S&\
J/R)L1T*M2U,O4W:^Eh=bGj!GchcqD%*!2ubchD*r!2ukchD*r!2uwc,D*T!2ctcqD%*!2cwcqD%\
* PubchD%I.*M2(0S,4W&/+36Ad:Eh8[C=bG7B<F!PckchD.t Puwc,D%I.Q(K0S&J/R)L1T*M2U\
,O4W:^Eh=bGj!PchcqD%* &wcbi%%I.Q*M(,&+)-56A:8[=b7<9>H &e&zi%.Q0S/1*M,+N-2UEh\
4G3F5XH &n&ni%%6.QAd*:2E &eczl%%I6Y*M2U+N<a3V(K0S)L1TDg,O=b Etcbi%%I.Q*M(K,O\
&+)-56YAd:^8[=b7<9>H EbcAi%.QAd0SCf/B1D*M+N Et&wi%6Y7Z*M2U,4+N3V-P5X Ebctr%%\
I6Y&J7Z*:2,O4+N3V-P5XHk Ebcwr%%I.Q(K0SCf&7/)1T*M:",
Concatenation(
"%%%%%k88b/8,%%%DM%%)%dAjdtA,,8!DJ,0ID=] )JU(:M%I6Y(K&)9.QAd0S/1D*M:^,O=b+<-\
> )JMdvM6Y87Z9]AdCBeDg*M,+N-P2U43V5X:^ )JUFXM6Y(K8[&7)9*M:^,O+->2UEh4W35H )J\
U%gM%I6Y(K8[.QAd0SCf*M:^,O=b2UEh4WGj %51.:/%.Q(0&)6Ad8C79*M+ %5/L:/%6Y*:(8,=\
.Q0 %51dV/%I(*M,:^=.Q02U4 %51,e/%.Q6Ad*2U:Eh %7J5:D%I.Q*2(,&)16A:E8[=79D %5J\
1vD.QAd0S/1D*M:^,+N->2UEh4 %6J0VD%6.Q %5J5wD%I.(K8[0C*M2,=4WGj %5M7vM%6Y(8&)\
.Q/*M,2U4 %5M5eM%6Y.Ad D51.:/%.Q(K0&)6YA8Cf79*M2U+ D5/L:/%6*:(8[,O=.0SCf D51\
dV/%I(K*M,O:^=b.Q0S2U4W D51,g/%I.Q6YAd*2U,4W:^E=bG D7,5:D%I.Q*2(,O&)16A:^Eh8\
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=b).Q2 /5DL:D*:(K8,=b.Q0Cf /5J(zD*M:^,O2UEh4W&J7Z /5L,gD*M(K8[,)L-0S4W1T5 /5\
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K*M:^,O.QAd0S2UEh4W /5U,gM%I6Y*M:^(8,O=b)-P0S4W15X M/7.:/%I.Q(0&)L6A8C79*M2U\
+N M//jv/IYK[JZL]QRe* M/7dV/I(K*M,:^=.Q02U4 M/7,g/%I.Q6YAd*M2U,O4W:E=G &57.",
"(/%I6Y*M:^&7.QAd2UEh/B(K8[,O=b)90SCf4WGj1D &5/jd/6YAd7ZBe:^Eh<aFi(K &57dF/6\
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+<->2UEh4WGj3F5H &57bI/%I6Y(K8[.QAd0SCf*M:^,O=b2UEh4WGj *57.(/%6*M:^&7.Q2U/(\
K,O)0SCf4G1D *5/jd/6Ad7Be:^E<Fi(K *57dD/6Y.QAd(K8[0SCf*M:^,O=b *57he/%I6Y.QA\
d*M:^2UEh&)L *57hI/&)L.0S/R1*:,O=b+<->2U4W35 H57.(/%6*M:&.Q/(K)0C4WG1 H55jb/\
.2U04W&J7Z H50%D/%I" ),
Concatenation(
"%%%%%k88d/8,,%%DM%%)%dAjdtA,,8 H)cz,cCf,O=b&7Z/Be+N<a) H)czeW(K.Q0*,+<-P>23\
V %Gwcd<%I.Q*2(,&+)1-56A:E8[=7<9D>H %GecC<.A0S/1D*:,+N->2UEh4 %Gnc4)%6.Q %Ge\
c}G%I.&7/B*M2+N<a3F(K0)91TDg,4W->5H DGtcd<%I.Q*2(,&)16A:E8[=79D DGbcm<%6*M(0\
,=4G DGtc><%.(K6A8*2,O+-P5X DGbcjY%I6Y(K8[*M2,=4WGj+<3F-5X /G)tv<%I.(0&/)16A\
8C7B9D*2U+3 /G)<v<%6*:(8,=IYM^K[Ob.A0C /G)b}e*M,2U4&J7/RB+N< /G)twY(06A8C*2U\
,4:E=G /2e8v<%I.(0&)6YA8C79*M+3 /2e)v<%I6*:(8,=.QAd0 /2e%}e*M,2U4&J7+N< /2e8\
eY*M26YA:^E /Pe8v<%I.(0S&/)16Ad8[C7B9D*2U+3 /Pe<v<%.(0&J/)1T6A8C7Be9]D*2+3V \
/Pe%}e*M,O2U4W&J7Z/RBe+N< /Pe8wY(06Ad8C*2U,4:^E=G %&wcd<%I.Q*(0,O&+3)-56A:^8\
[Cf=7<F9>H %&ecm<%6.Q*M:^2U(0C,4G %&wcw)%I.Q*M2U(K,O4W8[=bGj %&ec}G%I6Y.QAd*\
M:^2U+N<a3V(K0C)1TDg %&ecyY&J7Z/)91T*2UEh,O4G+<3->5X /&ett<%6Y*&.Q/3(,=b)0S1\
5 /&e,z<6YA7ZB:Eh<Fi(K /&ebze8[&7Z+<a)L9]1 /&eAeY(,6Y:^8=.Q20S4AdECGj DEtcd<\
%I.Q*(0,O&+3)-56A:^8[Cf=7<F9>H DEbcm<%I6Y.Q*:2U(0C,4G DEtcw)%I*26Y:E(K0S,O4W\
 DEbc}G%I6Y.QAd*M:^2U+N<a3V(K0C)1TDg DEbcyY&7/)91T*2E,O4G+<3->5X /Eett<%I6Y",
"*&+.Q2U/3(K,=)-0S415 /Ee<t<%I.(K06YA8Cf*M2,4:^E=G /Eebze(K8[,O=b&J7Z+N<a)91\
 /EetwY&J+.2/R3(,=)L-041T5 /Ee<wY%.(K06A8[C*2,O4:E=bG %*wcd<%I.Q*(K,4&/+)-56\
YAd:8[=G7B<9>H %*ecm<%I.A*M:^2U(0C,=4 %*wcw)%I.Q*M2U(K,O4W8[=bGj %*ecvY%I6Y.\
(K0C&7/)L1D*M2E,O=b4+3VFi->5X %*ecyG%I6Y.Q(K0SCf*M:^2UEh D*tcd<%I.Q*M(K,O4W&\
/+)-56YAd:^8[=bGj7B<9>H!D*bcm<.t D*tcw<%I.Q*M&/+N6YAd:^7B<a(K0" ),
Concatenation(
"%%%%%k88%/%,,%bDM%%)%dAjv}A,,8 EJ,1VB%^2UEh+N<a3VFi(K8[0SCf)L9]1TDg,O=b4WGj\
-P>c5XHk EJ,18r%%&IJ67YZ./QRABde*+MN:<^a23UV,-OP45WXGHjk 0JL(b-%%I6Y*M&+.QAd\
2U/3(K8[,O=b)- 0JFFb-%%I.(K0S6YA8[Cf*M2U,O4W 0JJ%tB%*M:^+N<a2UEh3VFi(K8[ 0JJ\
db6%*M&7+(K8[,O)->.Q2/R3V0S41T5X 0JL%k6%%I6Y(K.QAd0S*M:^,O2UEh4W %7J1%i%%I.Q\
*M(,&+)-56A:8[=b7<9>H %5J/ti%.QAd0C/B1D*M:^,=+<->2U %1J1Mi%.A*2(0,=4IQdMUKSO\
bW %5J1tl%%I6Y*M2+<3(K0)1D,O=b %7D4){%%I.Q*2&/+36A:^Eh7B<F(K0S,O4W %7S/&{D%I\
.Q*&+36A:^7<F(0,O %7S4*iD%I.Q*M2U(,&+)1-56A:E8[=b7<9D>H %7T4*iD%I*M(0,4&/+3)\
-6:8[Cf=bGj7B<F9> %7SR*iD%I*M(0,4&/+3)-6:8[Cf=bGj7B<F9> %7TR*iD%I.Q*M2U(,&+)\
1-56A:E8[=b7<9D>H %7%))z%%I.(06Ad8C*M2U!%5S4*rD&1 /75(&hD%I.Q*M2U(K,O&+)-6Y:\
^8[Cf=bGj7<9> /76(&hD%I.Q*M2U(K,O&+)-6Y:^8[Cf=bGj7<9> /71F&hD%I*M(,&J+N)L-P6\
:8[=b7Z<a9]>c.Q2U04/R3V1T5XAECfGjBeFiDgHk /5L%bi%%I6Y(K&).QAd0S/1*M:^,O=b+- \
/5FDbi%%I*(K,O6Y:8[=b.Q2U0S4W /5Jbki%%I6Y(K&7)*M:^,O+->.Q0/R1T2U43V5X /5L%t6\
%%I6Y&J7Z*M:^+N<a(8)L0C1T,=-P4G5X /5Sb&{D%I6Y*M&+.Q2/R3V(8)L!/55(&qD&1 )75(",
"&hD%I.Q*M2U(,&)16A8[Cf79D )76(&hD%I(K0S&/)16Y8[Cf7B<F9> )71D&hD%I*(K,O6Y:^8\
[=.Q2U0S4WAEhCGj!)55(&qD&1 275(&hD%I.Q*M2U(K,O&)16YAd8[Cf79D 276(&hD%I.Q(K0S\
&/)6Y:^8[Cf=bGj7B9 277D&hD%I(0&J/R)L6Y8[Cf7ZBe9]*M2U,O+N-P5X:E=b<a>cHk 25Jb&\
i%%I6Y*M(,.Q20S" ),
Concatenation(
"%%%%%k88b/8,%%DDM%%)%dAjdvA,,8 2,Jb7k3V(8)L 2,U(,n%I6Y(K&).QAd0S/1*M:^,O=b+\
- 2,Mdhn6Y87Z9]AdCBeDg*M 2,SdJn6Y(K&7)*M:^,O+->.Q0S/R1T2U43V5X 2,NEJn%I6.QAd\
 2,U%cn%I6Y(K8[.QAd0SCf*M:^,O=b2UEh4WGj!2,5,6e&1 E.5,5e%I.*M2(0S,4W&/+36Ad:E\
h8[C=bG7B<F!E,6,5e.t E.7J/e%I.Q(K0S&J/R)L1T*M2U,O4W:^Eh=bGj!E,5h6e%* H.5,5e%\
I.*M2(0S,4W&/+36Ad:Eh8[C=bG7B<F!H,6,5e.t H.7J/e%I.Q(K0S&J/R)L1T*M2U,O4W:^Eh=\
bGj!H,5h6e%* %LJ5,k%I.Q*M(,&+)-56A:8[=b7<9>H %JD7hk.Q0S/1*M,+N-2E4G3F5Hk!%ED\
6Jk-b %JJ7i/%I6Y*M2+<3(K0)1D,O=b )JU(,n%I6Y(K&)9.QAd0S/1D*M:^,O=b+<-> )JMdhn\
6Y87Z9]AdCBeDg*M,+N-P2U43V5X:^ )JUFJn6Y(K8[&7)9*M:^,O+->2UEh4W35H )JU%cn%I6Y\
(K8[.QAd0SCf*M:^,O=b2UEh4WGj %51.,e%.Q(0&)6Ad8C79*M+ %5/L,e%6Y*:(8,=.Q0 %51d\
J)%I(*M,:^=.Q02U4 %51,c)%.Q6Ad*2U:Eh %7J5,k%I.Q*2(,&)16A:E8[=79D %5J1hk.QAd0\
S/1D*M:^,+N->2UEh4 %6J0J/%6.Q %5J5i/%I.(80C*M2,=4G %/M7jn%I*M&+67.2AE(K0S /5\
L,,k%I6Y*(,O&).Q2U0S4/1 /5Jj%k(K,=).Q2 /5DL,k*:(K8,=b.0SC /5J(j/*M:^,O2UEh4W\
&J7Z /5L,ck*M(8,)L-0415X /5U,,n%6*M:^(K,&).Q2U04W/1 /5Sj%n(K8[,O=b).2U /5ML",
",n*:(8[,O=.Q0SCf /5SdJ2%I6Y(K*M:^,O.QAd0S2UEh4W /5U,cn%I6Y*M:^(8,=)-P041T5 \
&57.%e%I6Y*M:^&7.QAd2UEh/B(K8[,O=b)90SCf4WGj1D &5/jbe6YAd7ZBe:^Eh<aFi(K &52%\
D)%I" ),
Concatenation(
"%%%%%k88b/8,,%bDM8%)%dAjdtA,,8 &08a-,D&J7Z.QAd/RBe(K8[)L9]0SCf1TDg*M:^+N<a,\
O=b-P>c &08a85D%I(K&J)L.Q0S/R1T*M:^,O=b+<->2UEh4WGj3F5H &08a&5D%I6Y(K8[.QAd0\
SCf*M:^,O=b2UEh4WGj H08]A,D%6*M:&.Q/(K)0C4WG1 H08XC%D.2U04W&J7Z H08a(8D0SCf,\
O=b&7Z/Be+N<a) H08a95D(K.Q0*,+<->c23V /N9,Ai%%I.(0&)6YA8C79*+3 /N9&Ai%%I6*:(\
8,=.A0 /N9%Cu%*M,2U4&J7+< /N&,96%.AIYQd /*9AA-%%6Y*&.Q/3(,=)015 /*9(C-%6YA7Z\
B:E<F(K /*98C9%8[&7Z+<a)91 /*&.96%*2IQMU6A:EYd^h %3B8Vi%%I.Q*(K,4&/+)-56YAd:\
8[=G7B<9>H %398Yi%%I.A*M:^2U(0C,=4 %3B8^&%%I.Q*M2U(K,48[=G %398]r%%6.(K0C&J7\
Z/)L1D*M2E,=4+3F->5X %398^l%%I6Y.Q(K0SCf*M:^2UEh /39AA-%%I6Y*M&+.QAd2U/3(K8[\
,O=b)- /39-A-%%I.(K0S6YA8[Cf*M2U,O4W /398.B%*M:^+N<a2UEh3VFi(K8[ /39:A6%*M&7\
+(K8[,O)->.Q2/R3V0S41T5X /39A-6%%6(K.A0S*:,O2E4W %/VJAhD%I.Q(0&)6YAd8C79*M,O\
+- %/VEAhD%I6Y*:(8,=.Q2U04 %/VL-hD%I(&J)*M,+-P:^=<>c.Q0/R12U435X %/VJ:/D%I.Q\
6YAd*M2U:^Eh %/^8Vi%%I.Q*M2U(,&)16A:E8[=b79D %/^8Gi%%I.Q*M(,46YAd:^8=G %/^8K\
i%%I.Q(&J)16A8[79]Dg*M2U,+-P5X:E=b<a>H %/W8Fl%%I6Y*M:^.QAd2UEh %/WDL{D%I*&+",
"6Y:7<.Q2/3AdEBF(K0S D/VJAhD%.Q(0S&)6Ad8Cf79*M2U+ D/VEAhD%6*:(8[,=b.0SCf D/V\
L-bD%I(K*M,O:^=b.Q0S2U4W D/VJ:5D%.Q(0S6Ad8Cf*M2U:^Eh D/]8Vi%%I.Q*2(K,&)16YAd\
:E8[=79D D/V8Yi%%I6Y.QAd*M2U(,= D/]8Ki%%I.Q(K6YAd8[*M2U,O+N-P5X D/V8Xr%%I.(K\
8[0C&7/B)L1*M:^,O=b D/VDaBD%6Y&.Ad/*M2U(8[)9,O //WA8i%%I6Y*M(K,&).QAd2U0S4/1\
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S4WGj //WA:6%%I6Y*M&J7Z+N(K8[0SCf //W]8iD%I6Y*M:^(K,O&).Q" ),
Concatenation(
"%%%%%k88d/8,,%%b]A%,%dAjdtA,,8 /)N5T,:M6Y.QAd*M2U(, /)N5S-:M%I6Y.QAd*M:^2UE\
h(, /)N5ML:M%I6Y*:(K8[,O=b.Q2U0SCf4WGj /)N5SdXM%I6Y(K&J7Z)L*M:^,O+N-P>c.QAd0\
S/RBe1T2UEh4W3V5XHk /)N5U,gM%I6Y*M:^&J7Z+N<a(K8[)L9]0SCf1TDg M)N/7.:/%I.Q(0&\
)6A8C79]*M2U+N M)N//jv/IYK[JZL]QRe* M)N/5dX/I*M.Q204W6Y:AdE M)N/7,g/%I.Q(K0S\
*M,O:^=b *)N57.(/%6Y*M:&.QAd/B(K8[)90Cf4WG1 *)N55jb/.Q2U0S4W&J7Z *)N57bF/(K8\
[.QAd0SCf*M:^,O=b *)N57bg/%6Y&7Z.Ad/RB*M:^+N<a(K *)N57hI/(K.Q0S*M:^+<2Eh4WG3\
5 H)N57.(/%I6*M:&.QAd/(K8[)0SC4WG1 H)N55jb/.Q2U0S4W&J7Z H)N57bF/(K8[.QAd0SCf\
*M:^,O=b H)N57bg/%I6Y.QAd*M:^+N<a(K H)N57hI/(K.Q0S*:+N<a243VF5XH %GN7J5:D%I.\
Q*2(,&)16A:E8[=79D %GN5J1vD.A0S/1D*:,+N->2UEh4 %GN6J0VD%6.Q %GN5J/wD%I6Y*M:^\
.QAd2UEh DGN7,5:D%I.Q*2(,&)16A:E8[=79D DGN5,6:D%6*M(0,=4G DGN7,1XD%.(K6A8*2,\
O+-P5X DGN5,5yD%I.(K8[0C&7/B)L1*M:^,O=b /GN/L.:D%I.(0&)6A8C79*M2+3 /GN/DjvDI\
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5 /2N5DL:D%I6Y*:(8,=.QAd2E04 /2N5D(}D.Q2/R3AdEBFi(K /2N5F,gD.Q(K0S*M:^ /PN5",
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%& %&N5J5>D*,68:=.024IKMOY[^bQSUW %&N5J6[D%(68.024IKY[QSUW /&N5L.(D%6Y*:^&.Q\
Ad/3(8[,=b)0SCf15 /&N5DjdD6YAd7ZBe:^Eh<aFi(K /&N5JbjD:^+N<a2UEh3VFi(8[)9] /&\
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B %%)JJ6:D%I6Y*:(80C,4 %%)JJ7XD%I6Y(8&7/B)1*" ),
Concatenation(
"%%%%%k88%/%%%%%%G)%%%d}jv}Aj,8 (e8KF,DI*M2U(,&/6:E8[=b7B ()8J(JD%I6Y.Q*M2U(\
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 ()8JFJD%6(80,4IYK[SOW (%%/1J%%AId F&8.+,/%I6Y.Q(0&J7Z*M2U,=4G+N<a-> F08,+,/\
%I6Y.Q*2(K8[ F&8,+J/%I6Y.Q*M2U(K8[ F&<.+,/%.(K8[0SCf&7)L9]*:2,O4W+< F0<-+,/%\
6.*M2U(8 F&<-+J/%6.*M2U(8[ Ft8/4b/%I*M(.Q2U06:8[7<9] F&,/1h%%I.(K*M246Ad8:Eh\
Gj F88J(,D%I.Q*M2U(,&J/R)16YAd:^Eh8=7ZBe9D F88JF,D%I.Q(0&J/R+N3V)-6YAd8C7ZBe\
<aFi9> FV8J(,D%.*2(K,O&/)L1T6A:E8[=b7B9]Dg FV8JF,D%.(K0S&/+3)L-P6A8[Cf7B<F9]\
>c F98D+,M%I.Q*(K,46YAd:8[=G F&<,+J/%.*:2,=IQM^UOb F%8/4D/%6.IYQ!F%8JdJD(n D\
&8J+JM%I6Y.A*M2U D&8-+J/%*.2AEIYQU!DD8JdJD&7 1c8,+,/%I.Q*M2U(,&J)6:8[Cf=bGj7\
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Concatenation(
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Concatenation(
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Concatenation(
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gk!&O&%<-e&Y cO&88,e./012345ABCDEFGHIY EO&hA,)6Y*M&7Z0SCfGj1TD EO&hB,)%I6Y:^\
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Concatenation(
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