Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M32×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2220 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^70,c^b=cg1426 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2220×D71, C2×#22590453, #32151917, … |
| maximal normal subgroup of | #2220×D71, C2×#22590453, #32151917, … |
| maximal quotient of | #31911685, #31911736, #31911804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6623);