Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×#14556658 |
| Sylow | C73 ⋊ C22×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×#64408 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C22 | C23×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| hypercenter | C23×C4 | #64408 |
| hypocenter | C73 | C22×C4⋊C8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
640 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 640 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×#22624775, #34002345, C2×#22624809, … |
| maximal normal subgroup of | C2×#22624775, #34002345, C2×#22624809, … |
| maximal quotient of | C22×#17989449, C22×#17989451, C2×#22625480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21144);