Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#64408 |
| unambiguous semidirect product | D73⋊(C22×C42) |
| Fitting | C23×C4×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #64408 |
| commutator, hypocenter | C73 | C23×C42 |
| Frattini | C2 | C24×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C23×C4 | |
3000 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#64408)⋊#95, #34008315, #34008339, … |
| maximal normal subgroup of | (C2×#64408)⋊#95, #34008315, #34008339, … |
| maximal quotient of | C22×C42×#64408, C23×(C2×#64408)⋊C4, C22×#17989523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21480);