Finite Group DatabasebetaFinite Group Databasebeta| order | 30316 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D13×D53 |
| unambiguous semidirect product | (D13×C53)⋊(C2×C11) |
| unambiguous semidirect product | (C13×D53)⋊(C2×C11) |
| unambiguous semidirect product | D689⋊(C2×C11) |
| Fitting, socle, Hall | C11×C13×C53 ⋊ C22 |
| derived, Hall | C13×C53 ⋊ C22×C11 |
| Hall | C11×C53 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C11×D13 |
| Sylow | C13 ⋊ C2×C11×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D13×D53 |
| commutator, cosocle, hypocenter | C13×C53 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C53 | C22 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7579 |
2464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30316, 27);