Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#64408⋊C16 |
| unambiguous semidirect product | #64408⋊(C2×C16) |
| derived, Sylow | C73 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10596842 |
| commutator, hypocenter | C73 | C2×C4×C16 |
| Frattini | C4 | C22×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| socle | C22×C73 | C4×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C8 | |
216 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
272 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#10596842)⋊C16, #34032868, #34032921, … |
| maximal normal subgroup of | (C2×#10596842)⋊C16, #34032868, #34032921, … |
| maximal quotient of | C2×C8×#11924040, C8×#14556686, C2×#22626949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21664);