Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#99 (order 640) · Inn(G) = C22⋊AGL(1,𝔽5) · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C5 ⋊ C4 |
| 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:
(1,2,3,5,4)(6,8,9,13)(7,10,11,12);(2,3,4,5)(6,7)(8,12,13,10)(9,11)Polycyclic presentation:
2^5,5|a^2=c,b^2=e,b^a=bd,d^a=de,f^a=f^2,c^b=ce,f^c=f^419 conjugacy classes — view the full character table.
| maximal subgroup of | #64853, #64854, #64922, … |
| maximal normal subgroup of | #64853, #64854, #64922, … |
| maximal quotient of | #64853, #64854, #64855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 74);