Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#17989456 |
| Sylow | C73 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#64408 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | #95 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C2×#338 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 | |
372 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
620 conjugacy classes — view the full character table.
| maximal subgroup of | #34000535, #34000537, #34000543, … |
| maximal normal subgroup of | #34000535, #34000537, #34000543, … |
| maximal quotient of | C2×#22624756, C2×#22624757, #34002005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20183);