Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×#64408 |
| Fitting | C4⋊Q8×C73 ⋊ C4 |
| Sylow | C73 ⋊ C4×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Fitting | C4⋊Q8×C73 | C4 |
| hypercenter | C4⋊Q8 | #64408 |
| hypocenter | C73 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 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.
308 conjugacy classes — view the full character table.
| maximal subgroup of | #333×#64408, #332×#64408, #34003782, … |
| maximal normal subgroup of | #333×#64408, #332×#64408, #34003782, … |
| maximal quotient of | #389×#64408, #391×#64408, #384×#64408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20981);