Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C22×#14556645 |
| Fitting | C22×C8×C73 ⋊ C4 |
| Sylow | C73 ⋊ C22×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#64408 |
| commutator | C2×C73 | C22×C42 |
| Frattini | C4 | C23×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C23×C73 | C42 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C22×#97 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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 | #34008239, #34008242, #34008249, … |
| maximal normal subgroup of | #34008239, #34008242, #34008249, … |
| maximal quotient of | C22×#17989428, C2×#22625125, C22×#17989429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21061);