Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #2043 |
298 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^2=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,f^b=fg,h^b=h^70,e^c=eg,f^c=fg,h^c=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #2043×D71, C2×#22589585, #32025139, … |
| maximal normal subgroup of | #2043×D71, C2×#22589585, #32025139, … |
| maximal quotient of | #31900799, #31900804, #31900851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5755);