Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C112 · Schur multiplier (H2) = C2×C3×C11 |
| direct product | C2×C7×C112×C3⋊D3 |
| unambiguous semidirect product | (C2×C3)⋊(D3×C7×C112) |
| Fitting, socle | C2×C32×C7×C112 ⋊ C2 |
| derived, Sylow | C32 ⋊ C22×C7×C112 |
| Hall | C32×C7×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C22×C7 |
| Hall | C32×C7 ⋊ C22×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C112 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C22×C7×C112 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C112 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C7×C112 | |
840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15246 |
10164 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 491);