Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#17989520 |
| Sylow | C73 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C22×C16 |
| Frattini | C8 | C22×#64408 |
| Fitting | C2×C16×C73 | C4 |
| socle | C22×C73 | C2×C16 |
| hypercenter | C2×C16 | #64408 |
| hypocenter | C73 | C2×M64 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
112 conjugacy classes of subgroups.
656 conjugacy classes — view the full character table.
| maximal subgroup of | #34001053, #34001065, #34001084, … |
| maximal normal subgroup of | #34001053, #34001065, #34001084, … |
| maximal quotient of | C2×#22625039, C4×#17989520, C2×#22625045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20932);