Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C89 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D89 |
| commutator, socle | C23×C89 | C23 |
| Fitting | C2×C4⋊C4×C89 | C2 |
| hypercenter | C2×C4⋊C4 | D89 |
| hypocenter | C89 | #398 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^88902 conjugacy classes — view the full character table.
| maximal subgroup of | #26019246, #26019248, #26019253, … |
| maximal normal subgroup of | #26019246, #26019248, #26019253, … |
| maximal quotient of | #26018502, #26018503, #26018507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 480);