Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #358×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2186 |
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^70,d^b=df,f^b=fg,h^b=h^70,h^c=h^70799 conjugacy classes — view the full character table.
| maximal subgroup of | #2186×D71, C2×#22590266, #32151232, … |
| maximal normal subgroup of | #2186×D71, C2×#22590266, #32151232, … |
| maximal quotient of | #31909563, #31909907, #31910667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6436);