Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3322 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^70,c^b=cg,d^b=de,h^b=h^70,f^c=fg,h^d=h^701009 conjugacy classes — view the full character table.
| maximal subgroup of | #3322×D71, C2×#22600546, #32874401, … |
| maximal normal subgroup of | #3322×D71, C2×#22600546, #32874401, … |
| maximal quotient of | #32013057, #32013891, #32014683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 16716);