Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | Aut(G) = C2×AGL(1,𝔽5)×#120 (order 1280) · Inn(G) = C2×D5 · Out(G) = C2×C4×D4 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#168 |
| Sylow | C5 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,5,3)(7,9);(2,3)(4,5)(6,7)(8,9)(10,11,12,14,13,15,16,17)Polycyclic presentation:
2^5,5|a^2=c,c^2=e,b^a=bd,f^a=f^452 conjugacy classes — view the full character table.
| maximal subgroup of | #64671, #64672, #64688, … |
| maximal normal subgroup of | #64671, #64672, #64688, … |
| maximal quotient of | #64744, #64745, #64748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 37);