Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D712 |
| Fitting | C4×C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ C4×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D356 |
| commutator | C4×C89 | C22×C4 |
| Frattini | C2×C4 | C22×D89 |
| Fitting | C4×C8×C89 | C2 |
| socle | C22×C89 | C2×D4 |
| hypercenter | C4×C8 | D89 |
| hypocenter | C89 | C4×D8 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×C8 | |
134 conjugacy classes of subgroups.
1436 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26018212, #26018214, #26018218, … |
| maximal normal subgroup of | #26018212, #26018214, #26018218, … |
| maximal quotient of | C8×D712, #26019083, #26019138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 633);