Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #349 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊Dic89 |
| commutator | C22×C89 | C2×C8 |
| Frattini | C2×C8 | C2×D89 |
| Fitting | C2×M16×C89 | C2 |
| socle | C2×C89 | C22⋊C8 |
| hypercenter | C2×M16 | D89 |
| hypocenter | C89 | #349 |
| LCS | G ▷ C22×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ C2×M16 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^88,d^b=df902 conjugacy classes — view the full character table.
| maximal subgroup of | #26018187, #26018188, #26018189, … |
| maximal normal subgroup of | #26018187, #26018188, #26018189, … |
| maximal quotient of | #26018176, #26018192, #26018210, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 331);