Finite Group DatabasebetaFinite Group Databasebeta| order | 5696 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C89 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D89 |
| commutator, hypocenter | C89 | C64 |
| Fitting | C32×C89 | C2 |
| socle | C2×C89 | C32 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C32 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,89|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^881472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D89, C2×#19151317, #26018462, … |
| maximal normal subgroup of | C64×D89, C2×#19151317, #26018462, … |
| maximal quotient of | #26018071, C2×#19151317 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5696, 268);