Finite Group DatabasebetaFinite Group Databasebeta| order | 30316 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C13 · Schur multiplier (H2) = C2 |
| direct product | C22×C11×C53⋊C13 |
| unambiguous semidirect product | (C22×C53)⋊(C11×C13) |
| unambiguous semidirect product | (C22×C11×C53)⋊C13 |
| Fitting, socle, Hall | C22×C11×C53 ⋊ C13 |
| derived, Sylow | C53 ⋊ C22×C11×C13 |
| Hall | C11×C53 ⋊ C22×C13 |
| Hall | C22×C53 ⋊ C11×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C11 | C53⋊C13 |
| commutator, cosocle, hypocenter | C53 | C22×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C11×C53 | C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2332 |
748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30316, 20);