Finite Group DatabasebetaFinite Group Databasebeta| order | 31602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D229⋊C3) |
| unambiguous semidirect product | (C229⋊C3)⋊D23 |
| unambiguous semidirect product | D5267⋊C3 |
| Fitting, socle, derived, Hall | C23×C229 ⋊ C2×C3 |
| Hall | C23×C229⋊C3 ⋊ C2 |
| Hall | D5267 ⋊ C3 |
| Hall | C229⋊C3 ⋊ D23 |
| Sylow | C229 ⋊ C3×D23 |
| Sylow | C23 ⋊ D229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C229 | C2×C3 |
| LCS | G ▷ C23×C229 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 252 |
| transitive degree | μt(G) = 5267 |
A minimal faithful permutation representation — 2 generators on 252 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,29,30,26,27,31)(28,37,38,32,33,47)(34,50,51,40,41,64)(35,49,45,43,39,36)(42,69,70,53,54,87)(44,67,68,56,52,61)(46,48,66,58,59,62)(55,92,93,72,73,116)(57,90,91,75,71,84)(60,65,89,77,78,85)(63,105,103,81,82,80)(74,121,122,95,96,151)(76,119,120,98,94,113)(79,88,118,100,101,114)(83,134,135,106,107,109)(86,140,132,110,111,104)(97,156,157,124,125,192)(99,154,155,127,123,148)(102,117,153,129,130,149)(108,169,170,136,137,144)(112,176,174,141,142,139)(115,181,167,145,146,133)(126,197,198,159,160,232)(128,195,196,162,158,189)(131,152,194,164,165,190)(138,209,201,171,172,185)(143,215,216,177,178,180)(147,221,213,182,183,175)(150,224,207,186,187,168)(161,217,218,200,179,244)(163,234,235,202,199,230)(166,193,233,204,205,231)(173,240,237,210,211,227)(184,247,206,222,223,220)(188,248,239,225,226,214)(191,249,238,228,229,208)(203,245,246,236,219,251)(212,252,243,241,242,250);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,28,34,42,55,74,97,126,161,201,155,93,118,140,134,119,92,117,150,188,205,125,158,172,178,183,187,190,192,230,250,241,210,171,136,106,81,59,33,39,47,61,80,104,133,168,208,239,213,174,135,91,51,66,67,50,65,86,112,143,179,219,242,246,198,233,249,248,247,244,240,234,197,222,182,145,101,54,71,82,85,87,113,144,180,220,204,164,129,100,77,58,45,30,29,35,44,57,76,99,128,163,203,237,196,122,153,181,176,169,154,121,152,191,228,165,96,123,137,142,146,149,151,189,227,236,202,162,127,98,75,56,43,27,31,36,46,60,79,102,131,166,206,216,170,120,70,89,105,90,69,88,115,147,184,160,199,211,218,223,226,229,231,232,251,252,245,217,177,141,110,78,41,52,62,64,84,109,139,175,214,238,207,167,132,103,68,38,49,37,48,63,83,108,138,173,212,243,235,157,194,224,221,215,209,195,156,193,225,186,130,73,94,107,111,114,116,148,185,200,159,124,95,72,53,40,32,26)Polycyclic presentation:
2,3,23,229|c^a=c^22,d^a=d^228,d^b=d^134913 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31602, 12);