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Cayley diagramAliases
Subgroups
3048 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 20 points:
(1,2,3,4);(5,6,9,13,10,7,14,12)(8,11,17,19,16,15,20,18);(5,7)(6,10)(8,15)(9,12)(11,16)(13,14)(17,18)(19,20);(5,8,9,17,10,16,14,20)(6,11,13,19,7,15,12,18);(8,16)(11,15)(17,20)(18,19)
Conjugacy classes & character table
176 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | AGL(1,𝔽5)×#2956, C4×#61110, C4×#60182, … |
| maximal normal subgroup of | C4×#61110, C4×#60182, #72224754, … |
| maximal quotient of | AGL(1,𝔽5)×#2956, C2×C4×#2956, #72226894, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 6277292);
Finite Group Databasebeta