Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ #444 |
104 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)(6,9,12,20)(7,13,16,17)(8,15,18,14)(10,19,11,21);(6,8,12,18)(7,9,16,20)(10,17,11,13)(14,19,15,21);(2,3,4,5)(6,7,10,14,12,16,11,15)(8,9,17,19,18,20,13,21)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^2=f,d^2=f,e^2=f,c^a=cf,g^a=g^2,c^b=ce,e^b=ef,e^c=ef,g^d=g^429 conjugacy classes — view the full character table.
| maximal subgroup of | #10604132, #10604133, #10604138, … |
| maximal normal subgroup of | #10604132, #10604133, #10604138, … |
| maximal quotient of | #10603969, #10603971, #10603972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1079);