Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#18011961 |
| derived, Sylow | C149 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10597010 |
| commutator, hypocenter | C149 | C2×C32 |
| Frattini | C8 | C2×#10597010 |
| Fitting | C2×C8×C149 | C4 |
| socle, prime radical | C22×C149 | C16 |
| cosocle | #14558711 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C2×C8 | |
34 conjugacy classes of subgroups.
656 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#18011961, #34059796, #34059798, … |
| maximal normal subgroup of | C4×#18011961, #34059796, #34059798, … |
| maximal quotient of | C4×#18011961, C22⋊#18011961, C4⋊#18011961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 1479);