Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#11924040 |
| Sylow | C73 ⋊ D4⋊C16 |
110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 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=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^10,c^b=ce,h^d=h^27,h^f=h^72146 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#11924040, #34033697, #34033699, … |
| maximal normal subgroup of | C2×D4⋊#11924040, #34033697, #34033699, … |
| maximal quotient of | #34032781, #34032783, #34032785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21552);