Finite Group DatabasebetaFinite Group Databasebeta| order | 29118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D211⋊C3) |
| unambiguous semidirect product | (C211⋊C3)⋊D23 |
| unambiguous semidirect product | D4853⋊C3 |
| Fitting, socle, derived, Hall | C23×C211 ⋊ C2×C3 |
| Hall | C23×C211⋊C3 ⋊ C2 |
| Hall | D4853 ⋊ C3 |
| Hall | C211⋊C3 ⋊ D23 |
| Sylow | C211 ⋊ C3×D23 |
| Sylow | C23 ⋊ D211⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C211 | C2×C3 |
| LCS | G ▷ C23×C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 234 |
| transitive degree | μt(G) = 4853 |
A minimal faithful permutation representation — 2 generators on 234 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)(97,156,157,124,125,187)(99,154,155,127,123,148)(102,117,153,129,130,149)(108,164,165,136,137,144)(112,171,169,141,142,139)(115,176,162,145,146,133)(126,161,185,131,152,188)(128,189,190,159,158,184)(138,193,194,166,167,180)(143,200,201,172,173,175)(147,206,198,177,178,170)(150,211,192,181,182,163)(160,216,217,191,186,218)(168,219,220,195,196,215)(174,221,222,202,203,210)(179,225,224,207,208,205)(183,230,197,212,213,199)(204,231,232,223,214,233)(209,234,228,226,227,229);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,28,34,42,55,74,97,126,129,100,77,58,45,30,29,35,44,57,76,99,128,160,192,162,132,103,68,38,49,37,48,63,83,108,138,168,197,198,169,135,91,51,66,67,50,65,86,112,143,174,204,224,201,165,120,70,89,105,90,69,88,115,147,179,209,228,222,194,155,93,118,140,134,119,92,117,150,183,214,227,232,220,190,122,153,176,171,164,154,121,152,186,196,203,208,213,217,157,188,211,206,200,193,189,156,125,158,167,173,178,182,185,187,218,230,225,221,219,216,161,96,123,137,142,146,149,151,184,215,233,234,231,212,181,130,73,94,107,111,114,116,148,180,210,229,226,207,177,145,101,54,71,82,85,87,113,144,175,205,223,202,172,141,110,78,41,52,62,64,84,109,139,170,199,195,166,136,106,81,59,33,39,47,61,80,104,133,163,191,159,127,98,75,56,43,27,31,36,46,60,79,102,131,124,95,72,53,40,32,26)Polycyclic presentation:
2,3,23,211|c^a=c^22,d^a=d^210,d^b=d^196844 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29118, 12);