Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #333 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8,9,11,10,12,13,7)(15,19)(16,17)(20,21);(2,3)(4,5)(6,7,9,12,10,11,13,8)(14,15,17,19,18,21,16,20)Polycyclic presentation:
2^6,5|a^2=d,b^2=cd,c^2=ef,d^2=f,b^a=bc,c^a=ce,g^a=g^4,c^b=cf,d^b=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10598976, #10598984, #10598991, … |
| maximal normal subgroup of | #10598976, #10598984, #10598991, … |
| maximal quotient of | #10597971, #10598064, #10598065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 39);