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.
| Fitting | C5×M16 ⋊ C2 |
| 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)(6,7,8,11,9,10,12,13);(2,3)(4,5)(7,10)(8,12)Polycyclic presentation:
2^5,5|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 | D5×#100, #65038, #65040, … |
| maximal normal subgroup of | D5×#100, #65038, #65040, … |
| maximal quotient of | #64684, #64688, #64701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 30);