Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14559003 |
| Fitting | C22×D4×C151 ⋊ C2 |
| Sylow | C151 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D151 |
| commutator, cosocle | C2×C151 | C25 |
| Frattini | C2 | C24×D151 |
| Fitting | C22×D4×C151 | C2 |
| socle | C23×C151 | C23 |
| hypercenter | C22×D4 | D151 |
| hypocenter | C151 | C22×#41 |
| LCS | G ▷ C2×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
1540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34069026, #34069035, #34069047, … |
| maximal normal subgroup of | #34069026, #34069035, #34069047, … |
| maximal quotient of | C22×#18012695, C22×#18012697, C22×(C22⋊D151)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 1375);