Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #686 |
| automorphism | Aut(G) = C23×D4×AGL(1,𝔽5) (order 1280) · Inn(G) = C22⋊D5 · Out(G) = C23×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #106 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(11,14)(12,16)(15,17);(2,3)(4,5)(10,11,12,14,13,15,16,17)Polycyclic presentation:
2^5,5|a^2=d,b^2=c,d^2=e,b^a=bde,f^a=f^4,d^b=de34 conjugacy classes — view the full character table.
| maximal subgroup of | #65047, #65050, #65055, … |
| maximal normal subgroup of | #65047, #65050, #65055, … |
| maximal quotient of | #64700, #64707, #64714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 15);