Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#13083574 |
| Fitting | C23×C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D89 |
| commutator | C2×C89 | C25 |
| Frattini | C2 | C24×D89 |
| Fitting | C23×C4×C89 | C2 |
| socle | C23×C89 | C23 |
| hypercenter | C23×C4 | D89 |
| hypocenter | C89 | C22×#41 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
890 conjugacy classes of subgroups.
1448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26020163, #26020169, #26020178, … |
| maximal normal subgroup of | #26020163, #26020169, #26020178, … |
| maximal quotient of | C22×#15667969, C22×#15667971, C22×C4×C22⋊D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 1376);