Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#18012708 |
| Fitting | C25×C151 ⋊ C2 |
| Sylow | C151 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D151 |
| commutator, cosocle | C22×C151 | C24 |
| Frattini | C22 | C23×D151 |
| Fitting | C25×C151 | C2 |
| socle | C23×C151 | C23 |
| hypercenter | C25 | D151 |
| hypocenter | C151 | C2×#120 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ C25 | |
662 conjugacy classes of subgroups.
2428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34069515, #34069561, #34069563, … |
| maximal normal subgroup of | #34069515, #34069561, #34069563, … |
| maximal quotient of | C2×#23752068, C2×#23752085, C2×#23752091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 1035);