Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1953 |
184 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=f,b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,h^b=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31914090, #31914091, #31914125, … |
| maximal normal subgroup of | #31914090, #31914091, #31914125, … |
| maximal quotient of | #31896061, #31896066, #31896071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5298);