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Cayley diagramAliases
Subgroups
2219 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4);(5,6)(7,10,14,18)(8,15,16,11)(9,12)(13,17)(19,20);(5,7)(6,10,12,18)(8,13)(9,14)(11,17,15,20)(16,19);(5,8)(6,11)(7,13)(9,16)(10,17)(12,15)(14,19)(18,20)
Conjugacy classes & character table
116 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | C4×#12753, C4×#23895, AGL(1,𝔽5)×#1913, … |
| maximal normal subgroup of | C4×#12753, C4×#23895, C4×#23996, … |
| maximal quotient of | AGL(1,𝔽5)×#1913, C4×#9495, C2×C4×#1913 |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 261476);
Finite Group Databasebeta