Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#20294111 |
| Fitting, socle | C22×C433 ⋊ C16 |
| derived, Sylow | C433 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #20294111 |
| commutator, hypocenter | C433 | C22×C16 |
| Frattini | C1 | G |
| Fitting, socle | C22×C433 | C16 |
| prime radical | C22×D433 | C8 |
| cosocle | #16812367 | C23 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C22 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1732 |
172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 1681);