Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×#11924040 |
| derived, Sylow | C73 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10596842 |
| commutator, hypocenter | C73 | C8×C16 |
| Frattini | C2×C4 | C2×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| socle | C22×C73 | C4×C8 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C8 | |
104 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11924040, #34032750, #11924040⋊C16, … |
| maximal normal subgroup of | C16×#11924040, #34032750, #11924040⋊C16, … |
| maximal quotient of | C16×#11924040, #34032750, #34032856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21524);