Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#2196 (order 2560) · Inn(G) = C22⋊Dic5 · Out(G) = C4×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #100 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,4,5,3)(7,10)(8,12);(2,3)(4,5)(6,7,8,11,9,10,12,13)Polycyclic presentation:
2^5,5|a^2=c,c^2=e,b^a=bd,d^a=de,f^a=f^4,c^b=ce31 conjugacy classes — view the full character table.
| maximal subgroup of | #64691, #64692, #64756, … |
| maximal normal subgroup of | #64691, #64692, #64756, … |
| maximal quotient of | #64745, #64750, #64760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 40);