Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #431 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,8,10,9)(7,11,13,12)(14,17,18,16)(15,19,20,21);(14,16,18,17)(15,19,20,21);(2,3,4,5)(6,7,9,12,10,13,8,11)(14,15)(16,21)(17,19)(18,20)Polycyclic presentation:
2^6,5|a^2=d,b^2=e,c^2=ef,d^2=f,b^a=be,g^a=g^2,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598531, #10598549, #10598583, … |
| maximal normal subgroup of | #10598531, #10598549, #10598583, … |
| maximal quotient of | #10603789, #10603793, #10603829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1018);