Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1407 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^70,c^b=cf,d^b=defg,e^b=eg,d^c=dfg,e^d=eg574 conjugacy classes — view the full character table.
| maximal subgroup of | #1407×D71, C2×#22586500, #31917739, … |
| maximal normal subgroup of | #1407×D71, C2×#22586500, #31917739, … |
| maximal quotient of | #31884833, #31884871, #31884962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2670);