Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D112×C7⋊C9 |
| unambiguous semidirect product | (C11×D11)⋊(C2×C7⋊C9) |
| unambiguous semidirect product | (C7×D112)⋊C9 |
| derived, Hall | C7×C112 ⋊ C22×C9 |
| Hall | C112×C7⋊C9 ⋊ C22 |
| Hall | C7×D112 ⋊ C9 |
| Sylow | C112 ⋊ C22×C7⋊C9 |
| Sylow | C7 ⋊ C9×D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D112 |
| commutator, hypocenter | C7×C112 | C22×C9 |
| Fitting, socle, cosocle | C3×C7×C112 | C22×C3 |
| prime radical | C3×C7×D112 | C3 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C3 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 151);