Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #328×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1609 |
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^70,d^b=df,e^b=eg,h^b=h^70,d^c=dg,h^c=h^70688 conjugacy classes — view the full character table.
| maximal subgroup of | #1609×D71, C2×#22587340, #31969611, … |
| maximal normal subgroup of | #1609×D71, C2×#22587340, #31969611, … |
| maximal quotient of | #31886491, #31886496, #31886519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 3510);