Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1470 |
204 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 73 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=f,c^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^70,c^b=cg,e^b=ef,h^b=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #31889707, #31889709, #31889717, … |
| maximal normal subgroup of | #31889707, #31889709, #31889717, … |
| maximal quotient of | #31885800, #31885813, #31885826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2867);