Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #333×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1559 |
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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=g,c^2=f,d^2=g,e^2=fg,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^c=h^70691 conjugacy classes — view the full character table.
| maximal subgroup of | #1559×D71, C2×#22587067, #31965996, … |
| maximal normal subgroup of | #1559×D71, C2×#22587067, #31965996, … |
| maximal quotient of | #31885542, #31885561, #31885688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 3237);