Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11924746 |
| derived, Sylow | C149 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D149 |
| commutator, hypocenter | C149 | C82 |
| Frattini | C42 | C2×D149 |
| Fitting | C4×C8×C149 | C2 |
| socle, prime radical | C22×C149 | C42 |
| cosocle | C42×C149 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11924746, #34042607, #34042610, … |
| maximal normal subgroup of | C16×#11924746, #34042607, #34042610, … |
| maximal quotient of | #34042518, C16×#11924746, C8×#14558711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 269);