Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #576×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D73 |
| commutator | C4×C73 | C25 |
| Frattini | C4 | C24×D73 |
| Fitting | #576×C73 | C2 |
| socle | C2×C73 | C23×D4 |
| hypercenter | #576 | D73 |
| hypocenter | C73 | #3585 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #576 | |
1464 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^e=h^72833 conjugacy classes — view the full character table.
| maximal subgroup of | #33962226, #33962228, #33962240, … |
| maximal normal subgroup of | #33962226, #33962228, #33962240, … |
| maximal quotient of | #33949551, #33949563, #33949667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19285);