Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| automorphism | Aut(G) = D42×AGL(1,𝔽5) (order 1280) · Inn(G) = #685 · Out(G) = C22×C4 |
| 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)(6,8,9,15,10,16,18,21)(7,11,12,19,13,14,17,20);(2,3)(4,5)(6,7,10,13)(8,14,16,11)(9,17,18,12)(15,19,21,20)Polycyclic presentation:
2^5,5|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^4,d^b=de31 conjugacy classes — view the full character table.
| maximal subgroup of | #65034, #65037, D5×#101, … |
| maximal normal subgroup of | #65034, #65037, D5×#101, … |
| maximal quotient of | #64685, #64689, #64702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 31);