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Cayley diagramAliases
Subgroups
3861 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4);(5,6)(7,14,16,11)(8,10)(9,13)(12,17)(15,19,20,18);(6,10)(8,17)(11,18)(12,13)(14,19)(15,20);(5,7)(6,11)(8,15)(9,16)(10,18)(12,19)(13,14)(17,20)
Conjugacy classes & character table
116 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | AGL(1,𝔽5)×#1795, C4×#23882, C4×#23872, … |
| maximal normal subgroup of | C4×#23882, C4×#23872, D4×#1795, … |
| maximal quotient of | AGL(1,𝔽5)×#1795, #72257931, #72264021, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 262016);
Finite Group Databasebeta