Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×M16×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1980 |
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=df,c^2=e,d^2=g,b^a=bd,c^a=ce,h^a=h^70,d^b=dg,f^b=fg1438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31889331, #31889336, #31889352, … |
| maximal normal subgroup of | #31889331, #31889336, #31889352, … |
| maximal quotient of | #31896404, #31896408, #31896413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5429);