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Cayley diagramAliases
Subgroups
1500 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 12 points:
(3,4);(1,2)(3,4);(6,8)(10,11);(9,10,12,11);(5,6,7,8)(9,11,12,10)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227556, #72227941, #72227942, … |
| Frattini subgroup of | #93113, #93139, #93146, … |
| Fitting subgroup of | C22×#127⋊C3, A4×#127, #85647, … |
| maximal subgroup of | #8339, #8546, #10975, … |
| maximal normal subgroup of | #8339, #8546, #10975, … |
| maximal quotient of | C22×#384, C22×#390, C2×C4×#127, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2172);
Finite Group Databasebeta