Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #3227 |
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 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|b^2=e,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31893967, #31893969, #31894093, … |
| maximal normal subgroup of | #31893967, #31893969, #31894093, … |
| maximal quotient of | #32006937, #32007129, #32007964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15635);