Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3175 |
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^701012 conjugacy classes — view the full character table.
| maximal subgroup of | #32152556, #32152558, #32152601, … |
| maximal normal subgroup of | #32152556, #32152558, #32152601, … |
| maximal quotient of | #31998020, #32001722, #32001734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 15145);