Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | C22×(C2×#64408)⋊C4 |
| unambiguous semidirect product | D73⋊(C2×#95) |
| Fitting | C23×C4×C73 ⋊ C4 |
| Sylow | C73 ⋊ C22×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#64408 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C22 | C23×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| hypercenter | C23×C4 | #64408 |
| hypocenter | C73 | C22×#95 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1880 conjugacy classes of subgroups; only the 634 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 634 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×#64408)⋊#95, #34001291, #34001292, … |
| maximal normal subgroup of | (C2×#64408)⋊#95, #34001291, #34001292, … |
| maximal quotient of | C2×C4×(C2×#64408)⋊C4, C2×#22625104, C2×#22625105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20936);