Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #417×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2051 |
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^70,f^c=fg796 conjugacy classes — view the full character table.
| maximal subgroup of | #2051×D71, C2×#22589630, #32025333, … |
| maximal normal subgroup of | #2051×D71, C2×#22589630, #32025333, … |
| maximal quotient of | #31901128, #31901135, #31901156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5800);