Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D89 |
| commutator | C2×C89 | C22×C8 |
| Fitting | C4⋊C8×C89 | C2 |
| socle | C22×C89 | C22×C4 |
| hypercenter | C4⋊C8 | D89 |
| hypocenter | C89 | C8×D4 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=e,c^2=e,e^2=f,b^a=bd,g^b=g^88,g^c=g^88920 conjugacy classes — view the full character table.
| maximal subgroup of | #26019044, #26019046, #26019049, … |
| maximal normal subgroup of | #26019044, #26019046, #26019049, … |
| maximal quotient of | #26019046, #26019051, #26019058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 614);