Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #677 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#3003 (order 2560) · Inn(G) = D20 · Out(G) = C2×C4×D4 |
| 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)(10,11,12,14,13,15,16,17);(2,3)(4,5)(6,7,8,9)(11,14)(12,16)(15,17)Polycyclic presentation:
2^5,5|a^2=c,b^2=d,d^2=e,b^a=bd,d^a=de,f^a=f^446 conjugacy classes — view the full character table.
| maximal subgroup of | #64714, #64733, #64738, … |
| maximal normal subgroup of | #64714, #64733, #64738, … |
| maximal quotient of | #64677, #64733, #64771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 24);