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 ⋊ #441 |
108 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)(6,8,10,14)(7,11,13,20)(9,18,19,16)(12,21,17,15);(6,7,10,13)(8,15,14,21)(9,17,19,12)(11,18,20,16);(2,3,4,5)(8,14)(11,20)(15,21)(16,18)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,c^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 | #10604130, #10604131, #10604138, … |
| maximal normal subgroup of | #10604130, #10604131, #10604138, … |
| maximal quotient of | #10603970, #10603976, #10603977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1077);