Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#10596842 |
| Fitting | C2×Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ C2×C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C2×Q8×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C2×Q8 | #10596842 |
| hypocenter | C73 | C2×C8×Q8 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
440 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21750);