Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C5×C7 ⋊ C4 |
| Hall | C5×C7 ⋊ #99 |
| Sylow | C7 ⋊ #4011 |
| Sylow | C5 ⋊ #6408 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=c,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,c^b=ce,f^c=f^497 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 294);