Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C11 |
| direct product | C2×C3×ΓL(1,𝔽8)×C11⋊D11 |
| unambiguous semidirect product | (C2×C11)⋊(C3×ΓL(1,𝔽8)×D11) |
| Fitting, socle | C2×C3×C7×C112 ⋊ C2×C3 |
| derived, Hall | C7×C112 ⋊ C22×C32 |
| Hall | C3×C112×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C2×C7×C11⋊D11 ⋊ C32 |
| Sylow | C112 ⋊ C22×C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×C32×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | ΓL(1,𝔽8)×C11⋊D11 |
| commutator, cosocle, hypocenter | C7×C112 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C112 | C2×C3 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C2×C3 | |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5082 |
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 374);