Finite Group DatabasebetaFinite Group Databasebeta| order | 28158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D247 |
| Fitting, socle, derived, Hall | C13×C192 ⋊ C2×C3 |
| Hall | C13×C19×C19⋊C3 ⋊ C2 |
| Hall | C13⋊(C19⋊D19) ⋊ C3 |
| Hall | C19×C19⋊C3 ⋊ D13 |
| Sylow | C192 ⋊ C3×D13 |
| Sylow | C13 ⋊ (C19⋊C3)⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C192 | C2×C3 |
| LCS | G ▷ C13×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 741 |
A minimal faithful permutation representation — 2 generators on 51 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,19,20,16,17,21)(18,27,24,22,23,29)(25,30,32,31,28,26)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,18,24,30,27,31,17,21,26,32,20,19,25,23,28,29,22,16)(33,34,36,38,40,42,44,46,48,50,51,49,47,45,43,41,39,37,35)Polycyclic presentation:
2,3,13,19^2|c^a=c^12,d^a=d^18,e^a=e^18,d^b=d^71116 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28158, 73);