Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C7 ⋊ C4×Q8 |
| Sylow | C7 ⋊ C4×Dic10 |
| Sylow | C5 ⋊ #6450 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
Polycyclic presentation:
2^5,5,7|a^2=e,b^2=d,c^2=de,g^a=g^6,c^b=cde,f^b=f^4130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 339);