Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×#17989523 |
| unambiguous semidirect product | D73⋊#376 |
| Fitting | C2×C42×C73 ⋊ C4 |
| Sylow | C73 ⋊ C2×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#64408 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C22 | C23×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C42 | #64408 |
| hypocenter | C73 | C2×#376 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
656 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624754, #34001974, #34001981, … |
| maximal normal subgroup of | C2×#22624754, #34001974, #34001981, … |
| maximal quotient of | C2×C4×(C2×#64408)⋊C4, C4×#17989523, C2×#22625106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20937);