Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#23900 (order 5120) · Inn(G) = C2×D5 · Out(G) = #34655 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #117 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(11,15)(14,17);(10,12,13,16)(11,14,15,17);(2,3)(4,5)(6,7,8,9)(10,11)(12,14)(13,15)(16,17)Polycyclic presentation:
2^5,5|a^2=d,b^2=e,c^a=ce,f^a=f^452 conjugacy classes — view the full character table.
| maximal subgroup of | #64743, #64751, #64775, … |
| maximal normal subgroup of | #64743, #64751, #64775, … |
| maximal quotient of | #65214, #65215, #65221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 147);