Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#120 (order 640) · Inn(G) = #685 · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #99 |
52 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)(6,8)(7,10,11,12)(9,13);(2,3)(4,5)(6,7)(8,12)(9,11)(10,13)Polycyclic presentation:
2^5,5|b^2=c,b^a=bd,c^a=ce,f^a=f^4,d^b=de31 conjugacy classes — view the full character table.
| maximal subgroup of | #65029, #65030, #65031, … |
| maximal normal subgroup of | #65029, #65030, #65031, … |
| maximal quotient of | #64671, #64672, #64687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 13);