Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1765 |
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31912577, #31912582, #31915225, … |
| maximal normal subgroup of | #31912577, #31912582, #31915225, … |
| maximal quotient of | #31888129, #31888134, #31888146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4352);