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 ⋊ #101 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,10,16)(7,11,13,14)(9,17,18,15)(12,20,21,19);(2,3)(4,5)(6,7,9,12,10,13,18,21)(8,14,15,20,16,11,17,19)Polycyclic presentation:
2^5,5|a^2=c,b^2=e,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 | #64697, #64698, #64762, … |
| maximal normal subgroup of | #64697, #64698, #64762, … |
| maximal quotient of | #64748, #64750, #64763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 43);