Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C73 ⋊ #1710 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556587 |
| commutator | C42×C73 | C23 |
| Frattini | C42 | C22×D73 |
| Fitting | #500×C73 | C2 |
| socle | C22×C73 | #127 |
| hypercenter | #500 | D73 |
| hypocenter | C73 | #1710 |
| LCS | G ▷ C42×C73 ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^72,h^c=h^72830 conjugacy classes — view the full character table.
| maximal subgroup of | #33000293, #33000294, #33000297, … |
| maximal normal subgroup of | #33000293, #33000294, #33000297, … |
| maximal quotient of | #32979760, #32985728, #32985732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4119);