Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#15668009 |
| Fitting | C2×C42×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D89 |
| commutator | C22×C89 | C24 |
| Frattini | C22 | C23×D89 |
| Fitting | C2×C42×C89 | C2 |
| socle | C23×C89 | C23 |
| hypercenter | C2×C42 | D89 |
| hypocenter | C89 | C2×#127 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
1436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#19151341, #26018919, #26018921, … |
| maximal normal subgroup of | C2×#19151341, #26018919, #26018921, … |
| maximal quotient of | C2×#19151468, C2×#19151500, C4×#15668009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 1089);