Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D356 |
| Fitting | C4×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D89 |
| commutator, socle | C22×C89 | C24 |
| Fitting | C4×Q8×C89 | C2 |
| hypercenter | C4×Q8 | D89 |
| hypocenter | C89 | D4×Q8 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
905 conjugacy classes — view the full character table.
| maximal subgroup of | #26019353, #26019357, #26019415, … |
| maximal normal subgroup of | #26019353, #26019357, #26019415, … |
| maximal quotient of | Q8×#13083551, C4⋊C4×D356, Q8×C4⋊Dic89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 1216);