Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D433 |
| unambiguous semidirect product | C433⋊C26 |
| unambiguous semidirect product | (C2×C433)⋊C25 |
| Fitting, socle | C25×C433 ⋊ C2 |
| derived, Sylow | C433 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D433 |
| commutator, cosocle, hypocenter | C433 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C433 | C2 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13856 |
6976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1387);