Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #677 |
| automorphism | Aut(G) = C23×D4×AGL(1,𝔽5) (order 1280) · Inn(G) = D20 · Out(G) = C23×C4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ #102 |
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)(6,7,8,9)(10,11,12,14,13,15,16,17);(2,3)(4,5)(11,14)(12,16)(15,17)Polycyclic presentation:
2^5,5|b^2=cd,c^2=e,b^a=bc,c^a=ce,f^a=f^446 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#677, C4×D40, #64983, … |
| maximal normal subgroup of | C4×#677, C4×D40, #64983, … |
| maximal quotient of | #64679, #64690, #64705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 28);