Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C7 ⋊ M32 |
| Sylow | C7 ⋊ #3998 |
| Sylow | C5 ⋊ #6386 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^6,f^c=f^4124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 281);