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Cayley diagramAliases
Subgroups
337 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 12 points:
(3,4);(1,2)(3,4);(6,8)(9,10,11,12);(5,6)(7,8)(9,10)(11,12)
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #142216, #142217, #142218, … |
| Frattini subgroup of | #7187, #7213, #7250, … |
| Fitting subgroup of | A4×C22⋊C4, #73049, #85292, … |
| maximal subgroup of | C22⋊#95, #1437, #1438, … |
| maximal normal subgroup of | C22⋊#95, #1437, #1438, … |
| maximal quotient of | C22×#95, C2×C4×C22⋊C4, C2×#379, … |
| outer automorphism group of | C3×#125, #1572, #5000, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 193);
Finite Group Databasebeta