Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C73 ⋊ #3461 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | #537×C73 | C2 |
| hypercenter | #537 | D73 |
| hypocenter | C73 | #3461 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #537 | |
1012 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^72,h^e=h^72836 conjugacy classes — view the full character table.
| maximal subgroup of | #33058331, #33058337, #33058342, … |
| maximal normal subgroup of | #33058331, #33058337, #33058342, … |
| maximal quotient of | #33244676, #33244680, #33244940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17938);