Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×#64408 |
| Fitting | C32×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #64408 |
| commutator, hypocenter | C73 | C4×C32 |
| Frattini | C16 | C2×#64408 |
| Fitting | C32×C73 | C4 |
| socle | C2×C73 | C4×C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | C64×#64408, #34001203, C2×C32×#64408, … |
| maximal normal subgroup of | C64×#64408, #34001203, C2×C32×#64408, … |
| maximal quotient of | C32×#10596833, #34000756, #34001050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19613);