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 ⋊ #103 |
| Sylow | C7 ⋊ #4009 |
| Sylow | C5 ⋊ #6390 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|a^2=e,b^2=c,c^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,g^a=g^6,f^b=f^2,f^c=f^479 conjugacy classes — view the full character table.
| maximal subgroup of | #72217797, #72218135, AGL(1,𝔽5)×#1132, … |
| maximal normal subgroup of | #72217797, #72218135, AGL(1,𝔽5)×#1132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 223);