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Cayley diagramAliases
Subgroups
49 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);(17,18);(19,20)
Conjugacy classes & character table
64 conjugacy classes — view the full character table.
Relationships
| center of | #7465, #12539, C16×C22⋊C4, … |
| derived subgroup of | #93772, #93773, #93774, … |
| Frattini subgroup of | #7334, #7335, #7362, … |
| Fitting subgroup of | A4×C16, A4⋊C32, C16×S4, … |
| maximal subgroup of | #1374, #1379, #1380, … |
| maximal normal subgroup of | #1374, #1379, #1380, … |
| maximal quotient of | C2×C4×C16, C2×C22⋊C16, C2×C4⋊C16, … |
| automorphism group of | C8×C17, C3×C64, C3×C4×C17 |
| outer automorphism group of | C8×C17, C3×C64, C3×C4×C17, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 183);
Finite Group Databasebeta