Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C73 ⋊ #3563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | #539×C73 | C2 |
| hypercenter | #539 | D73 |
| hypocenter | C73 | #3563 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #539 | |
912 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,b^2=f,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^72,c^b=cg,d^b=df,h^c=h^72830 conjugacy classes — view the full character table.
| maximal subgroup of | #33059381, #33059387, #33059392, … |
| maximal normal subgroup of | #33059381, #33059387, #33059392, … |
| maximal quotient of | #33248940, #33248983, #33249233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19118);