Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#18012786 |
| Fitting | C2×#41×C151 ⋊ C2 |
| Sylow | C151 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D151 |
| commutator, cosocle | C2×C151 | C25 |
| Frattini | C2 | C24×D151 |
| Fitting | C2×#41×C151 | C2 |
| socle | C22×C151 | C24 |
| hypercenter | C2×#41 | D151 |
| hypocenter | C151 | C2×2−1+4 |
| LCS | G ▷ C2×C151 ▷ C151 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
794 conjugacy classes of subgroups.
1534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34069067, #34069070, #34069083, … |
| maximal normal subgroup of | #34069067, #34069070, #34069083, … |
| maximal quotient of | C2×#23752688, C2×#23752689, C2×#23752691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 1382);