Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #563×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3529 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | #563×C73 | C2 |
| hypercenter | #563 | D73 |
| hypocenter | C73 | #3529 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #563 | |
1058 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|e^2=f,b^a=bf,c^a=cg,d^a=dfg,h^a=h^72,c^b=cfg,d^b=df,h^b=h^72,h^d=h^72,h^e=h^72722 conjugacy classes — view the full character table.
| maximal subgroup of | #33067135, #33067141, #33067160, … |
| maximal normal subgroup of | #33067135, #33067141, #33067160, … |
| maximal quotient of | #33248598, #33248600, #33248622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 18651);