Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×#17989669 |
| derived, Sylow | C73 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10596842 |
| commutator, hypocenter | C73 | C2×C64 |
| Frattini | C8 | C2×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| socle | C22×C73 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C8 | |
40 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17989669, #34033146, #34033148, … |
| maximal normal subgroup of | C4×#17989669, #34033146, #34033148, … |
| maximal quotient of | C4×#17989669, C22⋊#17989669, C4⋊#17989669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21612);