Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#14558739 |
| derived, Sylow | C149 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10597010 |
| commutator, hypocenter | C149 | C22×C16 |
| Frattini | C4 | C22×#10597010 |
| Fitting | C22×C4×C149 | C4 |
| socle, prime radical | C23×C149 | C8 |
| cosocle | #11924746 | C23 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
656 conjugacy classes — view the full character table.
| maximal subgroup of | #34059729, #34059730, #34059745, … |
| maximal normal subgroup of | #34059729, #34059730, #34059745, … |
| maximal quotient of | C2×C4×#14558739, C2×C22⋊#14558739, C2×C4⋊#14558739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1602);