Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊#10596842 |
| unambiguous semidirect product | #64408⋊(C4⋊C8) |
| Fitting | C42×C73 ⋊ C8 |
| Sylow | C73 ⋊ C4×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#10596842 |
| commutator | C2×C73 | C2×C4×C8 |
| Frattini | C22 | C22×#10596842 |
| Fitting | C42×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C42 | #10596842 |
| hypocenter | C73 | C4×C4⋊C8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
316 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #34032727, #34032728, #34032736, … |
| maximal normal subgroup of | #34032727, #34032728, #34032736, … |
| maximal quotient of | C8×C4⋊#10596842, #34033283, #34033285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21647);