Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #330 |
60 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)(7,10,11,12)(14,16,17,15,19,20,18,21);(2,3)(4,5)(6,7)(8,10)(9,11)(12,13)(14,15,19,21)(16,17,20,18)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^4,d^b=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10599134, #10599137, #10599139, … |
| maximal normal subgroup of | #10599134, #10599137, #10599139, … |
| maximal quotient of | #10597968, #10597969, #10598150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 23);