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Cayley diagramAliases
Subgroups
660 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)(14,17)(15,19);(5,6,8,10)(7,9,11,12)(13,14)(15,18)(16,17)(19,20);(5,7)(6,9)(8,11)(10,12)(13,15,16,19)(14,18,17,20)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72235822, #72235838, #72235841, … |
| Frattini subgroup of | #93127, #93128, #93131, … |
| Fitting subgroup of | C22×#126⋊C3, A4×#126, #85646, … |
| maximal subgroup of | #8309, #8545, #8556, … |
| maximal normal subgroup of | #8309, #8545, #8556, … |
| maximal quotient of | C22×#383, C22×#387, C22×#388, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2170);
Finite Group Databasebeta