Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C22×#14556686 |
| derived, Sylow | C73 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10596842 |
| commutator, hypocenter | C73 | C23×C16 |
| Frattini | C2 | C23×#10596842 |
| Fitting | C22×C4×C73 | C8 |
| socle | C23×C73 | C2×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C22×C4 | |
440 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | #34034038, C2×#22627002, #34034044, … |
| maximal normal subgroup of | #34034038, C2×#22627002, #34034044, … |
| maximal quotient of | C22×C4×#11924040, C2×C4×#14556686, C2×#22627096, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21756);