Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ #117 |
| Sylow | C7 ⋊ #4018 |
| Sylow | C5 ⋊ #6435 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|b^2=e,c^2=d,c^a=ce,f^a=f^4,g^a=g^6292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 808);