Finite Group DatabasebetaFinite Group Databasebeta| order | 30316 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D143⋊D53 |
| unambiguous semidirect product | D583⋊D13 |
| unambiguous semidirect product | D689⋊D11 |
| Fitting, socle, derived, Hall | C11×C13×C53 ⋊ C22 |
| Hall | C13×C53 ⋊ C2×D11 |
| Hall | C11×C53 ⋊ C2×D13 |
| Hall | C11×C13 ⋊ C2×D53 |
| Sylow | C53 ⋊ D11×D13 |
| Sylow | C13 ⋊ D11×D53 |
| Sylow | C11 ⋊ D13×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C13×C53 | C22 |
| LCS | G ▷ C11×C13×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7579 |
Polycyclic presentation:
2^2,11,13,53|d^a=d^12,e^a=e^52,c^b=c^10,d^b=d^121954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30316, 39);