Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#10596842 |
| unambiguous semidirect product | #64408⋊(C4×C8) |
| Fitting | C42×C73 ⋊ C8 |
| derived, Sylow | C73 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #10596842 |
| commutator, hypocenter | C73 | C42×C8 |
| Frattini | C22 | C22×#10596842 |
| Fitting | C42×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C42 | |
408 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | #34032727, C4×C8×#10596842, C4×#17989671, … |
| maximal normal subgroup of | #34032727, C4×C8×#10596842, C4×#17989671, … |
| maximal quotient of | C4×C8×#10596842, C4×#17989671, #97×#10596842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21642);