Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#10596833 |
| derived, Sylow | C73 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #64408 |
| commutator, hypocenter | C73 | C42×C8 |
| Frattini | C23 | C22×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | #33999891, C4×C8×#10596833, C4×#17989428, … |
| maximal normal subgroup of | #33999891, C4×C8×#10596833, C4×#17989428, … |
| maximal quotient of | C4×C8×#10596833, C4×#17989428, #97×#10596833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20162);