Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | (C2×#10596842)⋊Q8 |
| Fitting | C2×Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1984 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#10596842 |
| commutator, socle | C22×C73 | C22×C8 |
| Fitting | C2×Q8×C73 | C8 |
| hypercenter | C2×Q8 | #10596842 |
| hypocenter | C73 | #1984 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
292 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^63,h^b=h^10,h^f=h^27,h^g=h^72146 conjugacy classes — view the full character table.
| maximal subgroup of | #34032978, #34033309, #34033354, … |
| maximal normal subgroup of | #34032978, #34033309, #34033354, … |
| maximal quotient of | #34033442, #34033443, #34033444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21661);