Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C89 ⋊ C2 |
| Sylow | C89 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D89 |
| commutator, socle | C2×C89 | C22×C8 |
| Fitting | M32×C89 | C2 |
| hypercenter | M32 | D89 |
| hypocenter | C89 | #504 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,d^2=e,e^2=f,g^a=g^88,c^b=cf,g^c=g^88920 conjugacy classes — view the full character table.
| maximal subgroup of | #26022086, #26022088, #26022091, … |
| maximal normal subgroup of | #26022086, #26022088, #26022091, … |
| maximal quotient of | #26021850, #26021851, #26021864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 967);