Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3482 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | D4×Q8×C73 | C2 |
| hypercenter | D4×Q8 | D73 |
| hypocenter | C73 | #3482 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1094 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=f,e^2=fg,b^a=bf,c^a=cg,h^a=h^72,d^b=df,h^c=h^72,h^e=h^72950 conjugacy classes — view the full character table.
| maximal subgroup of | #33061745, #33061753, #33061824, … |
| maximal normal subgroup of | #33061745, #33061753, #33061824, … |
| maximal quotient of | #33245441, #33245451, #33245464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 18131);