Finite Group DatabasebetaFinite Group Databasebeta| order | 27612 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C59⋊#261 |
| unambiguous semidirect product | C59⋊(C32×#261) |
| Fitting, socle, Hall | C32×C13×C59 ⋊ C4 |
| derived, Hall | C13×C59 ⋊ C32×C4 |
| Hall | C32×C59 ⋊ #261 |
| Hall | C32×C13 ⋊ Dic59 |
| Sylow | C59 ⋊ C32×#261 |
| Sylow | C13 ⋊ C32×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C59⋊#261 |
| commutator, hypocenter | C13×C59 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C59 | C4 |
| prime radical | C32×D13×C59 | C2 |
| cosocle | D13×C59 | C2×C32 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6903 |
2151 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27612, 88);