Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C5×C7 ⋊ #124 |
| Sylow | C7 ⋊ #4082 |
| Sylow | C5 ⋊ #6510 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|b^2=d,c^2=d,b^a=be,c^a=cd,g^a=g^6,c^b=cd,f^b=f^4112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 360);