Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×#11924036 |
| derived, Sylow | C73 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #64408 |
| commutator, hypocenter | C73 | C24×C8 |
| Frattini | C2 | C24×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C23×C4 | |
1976 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | #34008321, #34008324, #34008345, … |
| maximal normal subgroup of | #34008321, #34008324, #34008345, … |
| maximal quotient of | C23×C4×#10596833, C22×C4×#11924036, C22×#17989555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21494);