Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64868 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #329 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,5,4)(7,10)(8,12)(14,15,17,19)(16,20,21,18);(2,3,4,5)(6,7,8,11,9,10,12,13)(15,18,19,20)Polycyclic presentation:
2^6,5|a^2=c,b^2=f,c^2=ef,d^2=f,b^a=bd,d^a=def,g^a=g^2,c^b=ce,d^b=df,g^c=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10598575, #10598835, #10604431, … |
| maximal normal subgroup of | #10598575, #10598835, #10604431, … |
| maximal quotient of | #10598712, #10598722, #10598734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 265);