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 ⋊ #1949 |
240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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=f,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^70,d^b=dg1438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1949×D71, C2×#22589108, #32000912, … |
| maximal normal subgroup of | #1949×D71, C2×#22589108, #32000912, … |
| maximal quotient of | #31896039, #31896056, #31896093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5278);