Finite Group DatabasebetaFinite Group Databasebeta| order | 13124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C193 ⋊ C4 |
| Sylow | C193 ⋊ #595 |
| Sylow | C17 ⋊ #11715871 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C193 | C4 |
| prime radical, cosocle | D3281 | C2 |
| LCS | G ▷ C17×C193 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 210 |
| transitive degree | μt(G) = 3281 |
A minimal faithful permutation representation — 2 generators on 210 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,168)(128,159,160,182)(132,157,163,180)(136,166,167,177)(140,170,171,173)(144,174,175,169)(148,178,179,165)(152,181,176,162)(154,183,172,158)(161,184,185,189)(164,186,187,190)(188,191,192,193)(195,196,197,199)(198,201,202,206)(200,205,203,204)(207,209,210,208);(1,2,5,10,19,32,49,70,95,124,157,126,93,121,152,175,143,114,89,66,87,112,141,173,181,146,113,84,59,38,21,8,16,27,40,57,78,103,132,164,188,191,184,155,167,135,106,81,60,43,28,41,58,79,104,133,165,174,138,105,76,51,30,46,65,86,111,140,172,153,182,190,185,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,166,130,97,68,92,119,148,179,147,118,91,116,145,177,183,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,186,159,122,154,171,139,110,85,64,45,62,83,108,137,169,178,142,109,80,55,34,17,29,44,61,82,107,136,168,189,193,192,187,163,131,102,77,56,39,26,15,24,37,54,75,100,129,162,170,134,101,72,47,67,90,115,144,176,151,120,149,180,156,123,94,69,48,31,18,9,4)(194,195,198,203,199,204,208,210,206,201,207,209,205,196,200,202,197)Polycyclic presentation:
2^2,17,193|a^2=b,c^a=c^13,d^a=d^112,c^b=c^16,d^b=d^192824 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13124, 9);