Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#14556681 |
| derived, Sylow | C73 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10596842 |
| commutator, hypocenter | C73 | C22×C32 |
| Frattini | C4 | C22×#10596842 |
| Fitting | C22×C4×C73 | C8 |
| socle | C23×C73 | C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C22×C4 | |
120 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | #34033127, #34033128, #34033142, … |
| maximal normal subgroup of | #34033127, #34033128, #34033142, … |
| maximal quotient of | C2×C4×#14556681, C2×C22⋊#14556681, C2×C4⋊#14556681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21738);