Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×D73⋊M16 |
| unambiguous semidirect product | D73⋊(C22×M16) |
| Sylow | C73 ⋊ C23×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C23×C4×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C23×C4 | #64408 |
| hypocenter | C73 | C23×M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 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 | #34008325, #34008333, #34008336, … |
| maximal normal subgroup of | #34008325, #34008333, #34008336, … |
| maximal quotient of | C22×#17989546, C22×C4×#11924037, C2×C4×D73⋊M16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21496);