Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×#14556641 |
| derived, Sylow | C73 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #64408 |
| commutator, hypocenter | C73 | C22×C32 |
| Frattini | C8 | C22×#64408 |
| Fitting | C22×C8×C73 | C4 |
| socle | C23×C73 | C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C22×C8 | |
120 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | #34001051, #34001052, #34001067, … |
| maximal normal subgroup of | #34001051, #34001052, #34001067, … |
| maximal quotient of | C2×C4×#14556641, C2×C22⋊#14556641, C2×C4⋊#14556641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20928);