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 ⋊ #131 |
| Sylow | C7 ⋊ #4053 |
| Sylow | C5 ⋊ #6511 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=d,d^2=e,c^a=ce,g^a=g^6,c^b=ce,f^b=f^4118 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 393);