Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #330×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1529 |
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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,c^2=f,d^2=g,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^70,h^c=h^70697 conjugacy classes — view the full character table.
| maximal subgroup of | #1529×D71, C2×#22586946, #31965368, … |
| maximal normal subgroup of | #1529×D71, C2×#22586946, #31965368, … |
| maximal quotient of | #31885445, #31885458, #31885483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 3116);