Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D89 |
| commutator, socle | C23×C89 | C23 |
| Fitting | C22×Q8×C89 | C2 |
| hypercenter | C22×Q8 | D89 |
| hypocenter | C89 | #393 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
202 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^88902 conjugacy classes — view the full character table.
| maximal subgroup of | #26019202, #26019207, #26019229, … |
| maximal normal subgroup of | #26019202, #26019207, #26019229, … |
| maximal quotient of | #26018494, #26018511, #26018523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 460);