Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#21439062 |
| Fitting, socle, Hall | C2×C7×C192 ⋊ C3 |
| derived, Hall | C7×C192 ⋊ C2×C3 |
| Hall | C2×C192 ⋊ ΓL(1,𝔽8) |
| Sylow | C192 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ #11762245 |
| Sylow | C7 ⋊ C2×#11762245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21439062 |
| commutator, cosocle, hypocenter | C7×C192 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C192 | C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 ◁ C2 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5054 |
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44476497, #44476500, #44476506, … |
| maximal normal subgroup of | #44476497, #44476500, #44476506, … |
| maximal quotient of | C4×#21439062, C22×#21439062 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 82);