Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#13083549 |
| derived, Sylow | C89 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D89 |
| commutator, hypocenter | C89 | C22×C16 |
| Frattini | C8 | C22×D89 |
| Fitting | C22×C8×C89 | C2 |
| socle | C23×C89 | C8 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
1472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26018329, #26018330, #26018341, … |
| maximal normal subgroup of | #26018329, #26018330, #26018341, … |
| maximal quotient of | C2×C4×#13083549, C2×C22⋊#13083549, C2×C4⋊#13083549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 961);