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Cayley diagramAliases
Subgroups
596 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 20 points:
(3,4);(1,2)(3,4);(7,11)(9,12)(13,14,16,18)(15,17,19,20);(5,6,8,10)(7,9,11,12)(13,14)(15,17)(16,18)(19,20);(5,7)(6,9)(8,11)(10,12)(13,15,16,19)(14,17,18,20)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| Frattini subgroup of | #93118, #93121, #93123, … |
| Fitting subgroup of | A4×#125, #11711022, #11713295, … |
| maximal subgroup of | #8306, #8335, #8554, … |
| maximal normal subgroup of | #8306, #8335, #8554, … |
| maximal quotient of | C22×#382, C22×#387, C22×#389, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2169);
Finite Group Databasebeta