Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #686 |
| automorphism | Aut(G) = C22×D4×AGL(1,𝔽5) (order 640) · Inn(G) = C22⋊D5 · Out(G) = C22×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #104 |
44 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)(9,12)(11,13);(2,3)(4,5)(6,7,9,11,10,8,13,12)Polycyclic presentation:
2^5,5|a^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,d^b=de34 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#104, #65110, #65433, … |
| maximal normal subgroup of | D5×#104, #65110, #65433, … |
| maximal quotient of | #64752, D4⋊#168, Q8⋊#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 44);