Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #339 |
110 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)(11,14,15,16);(2,3)(4,5)(6,7,8,9)(10,11)(12,14)(13,15)(16,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,e^a=ef,g^a=g^492 conjugacy classes — view the full character table.
| maximal subgroup of | #10599438, #10599439, #10599487, … |
| maximal normal subgroup of | #10599438, #10599439, #10599487, … |
| maximal quotient of | #10598102, #10598103, #10598106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 81);