Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#14556681 |
| derived, Sylow | C73 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #10596842 |
| commutator, hypocenter | C73 | C4×C32 |
| Frattini | C2×C4 | C2×#10596842 |
| Fitting | C42×C73 | C8 |
| socle | C22×C73 | C2×C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C42 | |
72 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14556681, #34032995, #34033001, … |
| maximal normal subgroup of | C8×#14556681, #34032995, #34033001, … |
| maximal quotient of | C8×#14556681, #34033001, #34033127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21592);