Finite Group DatabasebetaFinite Group Databasebeta| order | 30316 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic53⋊C13) |
| unambiguous semidirect product | Dic583⋊C13 |
| derived, Hall | C11×C53 ⋊ C4×C13 |
| Hall | C11×C53⋊C13 ⋊ C4 |
| Hall | Dic583 ⋊ C13 |
| Hall | C53⋊C13 ⋊ Dic11 |
| Sylow | C53 ⋊ C13×Dic11 |
| Sylow | C11 ⋊ Dic53⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(D53⋊C13) |
| commutator, hypocenter | C11×C53 | C4×C13 |
| Fitting, socle, cosocle | C2×C11×C53 | C2×C13 |
| prime radical | C2×C11×C53⋊C13 | C2 |
| LCS | G ▷ C11×C53 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2332 |
Polycyclic presentation:
2,11,13,53,2|a^2=e,b^a=b^10,d^a=d^52,d^c=d^16226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30316, 12);