Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #417×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1792 |
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,d^c=dg,h^c=h^70802 conjugacy classes — view the full character table.
| maximal subgroup of | #1792×D71, C2×#22588292, #31996746, … |
| maximal normal subgroup of | #1792×D71, C2×#22588292, #31996746, … |
| maximal quotient of | #31888849, #31888859, #31888961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4462);