Finite Group DatabasebetaFinite Group Databasebeta| order | 28158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | (C13⋊C3)⋊(C19⋊D19) |
| Fitting, socle, derived, Hall | C13×C192 ⋊ C2×C3 |
| Hall | C192×C13⋊C3 ⋊ C2 |
| Hall | C13⋊(C19⋊D19) ⋊ C3 |
| Sylow | C192 ⋊ D13⋊C3 |
| Hall | C13⋊C3 ⋊ C19⋊D19 |
| Sylow | C13 ⋊ C3×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C192 | C2×C3 |
| LCS | G ▷ C13×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4693 |
A minimal faithful permutation representation — 3 generators on 51 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51);(1,2,5,4,8,11,10,12,13,7,6,9,3)(33,34,36,38,40,42,44,46,48,50,51,49,47,45,43,41,39,37,35);(14,15,17,19,21,23,25,27,29,31,32,30,28,26,24,22,20,18,16)Polycyclic presentation:
2,3,13,19^2|c^a=c^12,d^a=d^18,e^a=e^18,c^b=c^31268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28158, 54);