Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #3993 |
| automorphism | Aut(G) = AGL(1,𝔽5)×AGL(1,ℤ/8) (order 640) · Inn(G) = C4⋊AGL(1,𝔽5) · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #108 |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(6,8,10,17,11,18,9,16)(7,12,13,15,14,20,19,21);(2,3,4,5)(6,7,9,13,11,14,10,19)(8,15,16,20,18,21,17,12)Polycyclic presentation:
2^5,5|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,f^c=f^422 conjugacy classes — view the full character table.
| maximal subgroup of | #64847, ΓL(1,𝔽81), #64906, … |
| maximal normal subgroup of | #64847, ΓL(1,𝔽81), #64906, … |
| maximal quotient of | #64881, #64884, #64896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 70);