Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C7⋊#170) |
| Hall | C5×C7 ⋊ C4⋊C8 |
| Sylow | C7 ⋊ C4⋊#170 |
| Sylow | C5 ⋊ C4⋊(C7⋊C8) |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1120 |
Polycyclic presentation:
2^5,5,7|a^2=c,b^2=d,c^2=e,b^a=bd,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, 286);