Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1842 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C42×C73 | C8 |
| hypercenter | C42 | #10596842 |
| hypocenter | C73 | #1842 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 | |
300 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,b^2=d,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^10,h^f=h^27,h^g=h^72200 conjugacy classes — view the full character table.
| maximal subgroup of | #34032745, #34033317, #34033318, … |
| maximal normal subgroup of | #34032745, #34033317, #34033318, … |
| maximal quotient of | #34033346, #34033347, #34033348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21654);