Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×#64408 |
| unambiguous semidirect product | D73⋊C43 |
| Fitting | C2×C42×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #64408 |
| commutator, hypocenter | C73 | C2×C43 |
| Frattini | C22 | C23×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C42 | |
1272 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624758, #34002030, #34002037, … |
| maximal normal subgroup of | C2×#22624758, #34002030, #34002037, … |
| maximal quotient of | C43×#64408, C2×#95×#64408, C2×C4×(C2×#64408)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20935);