Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #443 |
106 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)(7,13)(8,14)(10,18)(11,12)(15,16)(17,21)(19,20);(6,8)(7,12)(9,15)(10,16)(11,17)(13,20)(14,19)(18,21);(2,3)(4,5)(6,7,10,14,11,15,20,21)(8,12,16,19,17,9,13,18)Polycyclic presentation:
2^6,5|a^2=d,d^2=f,e^2=f,g^a=g^4,c^b=ce,e^b=ef,e^c=ef56 conjugacy classes — view the full character table.
| maximal subgroup of | #10598815, #10598816, #10600031, … |
| maximal normal subgroup of | #10598815, #10598816, #10600031, … |
| maximal quotient of | #10601080, #10601082, #10601084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 823);