Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #568×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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=g,f^2=g,b^a=be,e^a=eg,f^b=fg,h^b=h^70,d^c=dg1231 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32006623, #32006625, #32006629, … |
| maximal normal subgroup of | #32006623, #32006625, #32006629, … |
| maximal quotient of | #31963274, #31963279, #31963363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 12992);