Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#15667951 |
| Fitting | C2×C16×C89 ⋊ C2 |
| Sylow | C89 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D89 |
| commutator | C2×C89 | C22×C8 |
| Frattini | C8 | C22×D89 |
| Fitting | C2×C16×C89 | C2 |
| socle | C22×C89 | C2×C8 |
| hypercenter | C2×C16 | D89 |
| hypocenter | C89 | C2×M32 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
90 conjugacy classes of subgroups.
1448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26018391, C4×#15667951, #26021845, … |
| maximal normal subgroup of | #26018391, C4×#15667951, #26021845, … |
| maximal quotient of | C2×#19151373, C4×#15667951, C2×#19151377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 963);