Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #556×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3324 |
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^70904 conjugacy classes — view the full character table.
| maximal subgroup of | #31987070, #31987072, #31987130, … |
| maximal normal subgroup of | #31987070, #31987072, #31987130, … |
| maximal quotient of | #32013061, #32013923, #32014712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 16735);