Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #3240 |
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^c=h^701006 conjugacy classes — view the full character table.
| maximal subgroup of | #31894667, #31894669, #31978829, … |
| maximal normal subgroup of | #31894667, #31894669, #31978829, … |
| maximal quotient of | #32006990, #32007200, #32008028, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15746);