Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C7 ⋊ #99 |
| Sylow | C7 ⋊ #3966 |
| Sylow | C5 ⋊ #6380 |
104 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|b^2=c,b^a=bd,c^a=ce,g^a=g^6,d^b=de,f^b=f^4109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 71);