Finite Group DatabasebetaFinite Group Databasebeta| order | 160 |
| isoclinism | isoclinic class of #3958 |
| automorphism | Aut(G) = AGL(1,𝔽5)×#442 (order 1280) · Inn(G) = #686 · Out(G) = C42 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ SD32 |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,7,10,13)(8,15,17,21)(9,18,16,12)(11,19,20,14);(2,3)(4,5)(7,11)(8,14)(9,16)(12,21)(13,20)(15,18)(17,19)Polycyclic presentation:
2^5,5|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^4,c^b=cd,d^b=de25 conjugacy classes — view the full character table.
| maximal subgroup of | D5×SD32, #65203, #65207, … |
| maximal normal subgroup of | D5×SD32, #65203, #65207, … |
| maximal quotient of | #64710, #64711, #64784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(160, 35);