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Cayley diagramAliases
Subgroups
249 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 12 points:
(1,2,3,4);(5,6,7,8);(9,10);(11,12)
Conjugacy classes & character table
64 conjugacy classes — view the full character table.
Relationships
| center of | C2×#1273, C4×#336, C4×#376, … |
| derived subgroup of | C22⋊(C42⋊C3), #1437⋊C3, C2×C22⋊(C42⋊C3), … |
| Frattini subgroup of | #7016, #7017, #7020, … |
| Fitting subgroup of | C22×C42⋊C3, C42×A4, C22⋊(C42⋊C3), … |
| socle of | C2×#7633646, #72262085, C4×#34736, … |
| maximal subgroup of | C4×#95, #1434, C4⋊#95, … |
| maximal normal subgroup of | C4×#95, #1434, C4⋊#95, … |
| maximal quotient of | C2×C43, C22×#95, C2×#376, … |
| automorphism group of | C3×C5×C16 |
| outer automorphism group of | C3×C5×C16, #7068, #7069, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 192);
Finite Group Databasebeta