Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #125×D89 |
| Fitting | #125×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | #125×C89 | C2 |
| hypercenter | #125 | D89 |
| hypocenter | C89 | C2×#125 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #125 | |
226 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | #330×D89, #26018852, #26018877, … |
| maximal normal subgroup of | #330×D89, #26018852, #26018877, … |
| maximal quotient of | #382×D89, #387×D89, #389×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 1068);