Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3151 |
656 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 153 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=f,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^70802 conjugacy classes — view the full character table.
| maximal subgroup of | #32024024, #32024028, #32048434, … |
| maximal normal subgroup of | #32024024, #32024028, #32048434, … |
| maximal quotient of | #31985289, #31985293, #31985296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 14958);