Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C7 ⋊ #106 |
| Sylow | C7 ⋊ #3993 |
| Sylow | C5 ⋊ #6382 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=d,b^2=c,d^2=e,b^a=bde,g^a=g^6,d^b=de,f^b=f^2,f^c=f^464 conjugacy classes — view the full character table.
| maximal subgroup of | #72217780, #72218110, #72218131, … |
| maximal normal subgroup of | #72217780, #72218110, #72218131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 228);