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Cayley diagramAliases
Subgroups
1182 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2);(3,4)(5,6)(7,8,12,16,14,17,13,20)(9,11,18,22,19,10,15,21);(4,6)(7,9,11,16,13,18,21,17,14,19,10,20,12,15,22,8);(7,10,12,21,14,11,13,22)(8,15,16,9,17,18,20,19)
Conjugacy classes & character table
92 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | C2×C4×AGL(1,ℤ/16), C2×#495949, C2×#495843, … |
| maximal normal subgroup of | C2×C4×AGL(1,ℤ/16), C2×#495949, C2×#495843, … |
| maximal quotient of | C2×#128688, C2×#128691, C2×#128557, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 400279);
Finite Group Databasebeta