Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×C73 ⋊ C4 |
| Sylow | C73 ⋊ #2179 |
144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 46 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=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^27,d^b=df,f^b=fg,h^c=h^27,h^e=h^72230 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22626333, D73⋊#2179, #34030277, … |
| maximal normal subgroup of | C2×#22626333, D73⋊#2179, #34030277, … |
| maximal quotient of | #34011866, #34011869, #34011871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20912);