Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#10596833 |
| derived, Sylow | C73 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #64408 |
| commutator, hypocenter | C73 | C22×C4×C8 |
| Frattini | C22 | C23×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C24×C73 | C2×C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C23×C4 | |
760 conjugacy classes of subgroups; only the 498 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 498 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
704 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624753, #34001955, #34001959, … |
| maximal normal subgroup of | C2×#22624753, #34001955, #34001959, … |
| maximal quotient of | C22×C8×#10596833, C22×#17989428, C2×M16×#10596833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21059);