Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#14556688 |
| Sylow | C73 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#10596842 |
| commutator | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C22×C4×C73 | C8 |
| socle | C23×C73 | C2×C8 |
| hypercenter | C22×C4 | #10596842 |
| hypocenter | C73 | C22×M32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
400 conjugacy classes of subgroups.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #34034041, #34034044, C2×#22627006, … |
| maximal normal subgroup of | #34034041, #34034044, C2×#22627006, … |
| maximal quotient of | C22×#17989681, C2×C4×#14556688, C22×#17989684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21759);