Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C192 ⋊ C2×C3 |
| Hall | C19×#87705 ⋊ C2 |
| Hall | C7⋊(C19⋊D19) ⋊ C3 |
| Sylow | C192 ⋊ AGL(1,𝔽7) |
| Sylow | C7 ⋊ (C19⋊C3)⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 399 |
A minimal faithful permutation representation — 2 generators on 45 points:
(2,5,6,3,4,7)(9,13,14,10,11,15)(12,20,21,16,17,25)(18,26,24,23,22,19)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45);(1,2,4,7,6,5,3)(8,9,12,17,22,25,24,14,13,18,23,11,15,19,21,26,20,16,10)(27,28,30,32,34,36,38,40,42,44,45,43,41,39,37,35,33,31,29)Polycyclic presentation:
2,3,7,19^2|c^a=c^6,d^a=d^18,e^a=e^18,c^b=c^2,d^b=d^11451 conjugacy classes — view the full character table.
| maximal subgroup of | #11716326⋊D19, D19×#11716328, #11716322⋊D19, … |
| maximal normal subgroup of | #11716326⋊D19, D19×#11716328, #11716322⋊D19, … |
| maximal quotient of | #44476505, C2×#29503113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 48);