Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ #123 |
| Sylow | C7 ⋊ #4075 |
| Sylow | C5 ⋊ #6492 |
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|c^2=e,b^a=be,c^a=cd,f^a=f^4,g^a=g^6286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 865);