Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#125×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3080 |
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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=e,b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31894540, #31894546, #31894547, … |
| maximal normal subgroup of | #31894540, #31894546, #31894547, … |
| maximal quotient of | #31996950, #31998427, #31999631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 14328);