Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#108 |
| Sylow | C5 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,9,10,17,11,18,8,15)(7,13,12,16,14,20,19,21);(6,8,11,10)(7,12,14,19)(9,15,18,17)(13,16,20,21);(2,3,4,5)(6,7,8,12,11,14,10,19)(9,16,15,20,18,21,17,13)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^2,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #10598603, #10598606, #10598625, … |
| maximal normal subgroup of | #10598603, #10598606, #10598625, … |
| maximal quotient of | D5⋊#334, D5⋊#335, #10603820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1062);