Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#106×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2065 |
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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=de,b^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^c=dg,e^c=eg,f^c=fg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #2065×D71, C2×#22589709, #32026063, … |
| maximal normal subgroup of | #2065×D71, C2×#22589709, #32026063, … |
| maximal quotient of | #31901964, #31901985, #31902020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5879);