Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #3181 |
366 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 366 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|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^70,d^c=dg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31895021, #31895023, #31978829, … |
| maximal normal subgroup of | #31895021, #31895023, #31978829, … |
| maximal quotient of | #31998044, #32001774, #32001785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15220);