Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #2047 |
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^70,c^b=cf,d^b=dg,h^b=h^70,e^c=eg,f^c=fg,h^c=h^701006 conjugacy classes — view the full character table.
| maximal subgroup of | #31909945, #31909950, #31909956, … |
| maximal normal subgroup of | #31909945, #31909950, #31909956, … |
| maximal quotient of | #31901063, #31901070, #31901119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5779);