Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| 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:
(1,2,4,5,3)(6,9)(7,14)(8,16)(10,20)(11,21)(12,13)(15,18)(17,19);(6,8)(7,13)(9,17)(10,14)(11,19)(12,18)(15,21)(16,20);(2,3)(4,5)(6,7,10,15,12,17,11,16)(8,13,14,21,18,9,19,20)Polycyclic presentation:
2^6,5|a^2=d,d^2=f,e^2=f,c^a=cf,g^a=g^4,c^b=ce,e^b=ef,e^c=ef50 conjugacy classes — view the full character table.
| maximal subgroup of | #10600041, #10600042, #10602308, … |
| maximal normal subgroup of | #10600041, #10600042, #10602308, … |
| maximal quotient of | #10601081, #10601083, #10601084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 824);