Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#17989643 |
| Sylow | C73 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C4 | C23×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C22×M32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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 | #34012108, #34012112, #34012118, … |
| maximal normal subgroup of | #34012108, #34012112, #34012118, … |
| maximal quotient of | C2×#22626132, C4×#17989643, C2×#22626137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21472);