Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #336×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2071 |
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^70,f^c=fg,h^c=h^701432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31886476, #31886477, #31886482, … |
| maximal normal subgroup of | #31886476, #31886477, #31886482, … |
| maximal quotient of | #31902154, #31902159, #31902174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5915);