Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #518×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator | C2×C73 | C24×C4 |
| Fitting | #518×C73 | C2 |
| socle | C22×C73 | C25 |
| hypercenter | #518 | D73 |
| hypocenter | C73 | C4×H(5,𝔽2) |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #518 | |
1660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=g,e^2=g,b^a=bf,d^a=df,c^b=cf,h^e=h^721292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33091857, #33091863, #33091868, … |
| maximal normal subgroup of | #33091857, #33091863, #33091868, … |
| maximal quotient of | #33244214, #33244218, #518×Dic73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17714);