Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #338 |
86 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)(6,8,9,18,11,19,10,17)(7,12,14,16,15,20,13,21);(2,3)(4,5)(6,7,9,13,11,15,10,14)(8,16,17,20,19,21,18,12)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,d^2=f,e^2=f,b^a=be,d^a=df,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10598026, #10598028, #10598270, … |
| maximal normal subgroup of | #10598026, #10598028, #10598270, … |
| maximal quotient of | #10598151, #10598161, #10598170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 118);