Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #416×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3136 |
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^70,d^b=dg,h^b=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #32067397, #32067401, #32067427, … |
| maximal normal subgroup of | #32067397, #32067401, #32067427, … |
| maximal quotient of | #31997662, #32000104, #32000118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 14868);