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Cayley diagramAliases
Subgroups
2758 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 20 points:
(1,2,3,4,5,6,7,8);(2,8)(3,7)(4,6);(10,12)(14,17)(15,19);(13,14)(15,18)(16,17)(19,20);(9,10)(11,12)(13,15,16,19)(14,18,17,20)
Conjugacy classes & character table
98 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | #72305391, D8×#525, #123×AGL(1,ℤ/8), … |
| maximal normal subgroup of | #72305391, D8×#525, #123×AGL(1,ℤ/8), … |
| maximal quotient of | #72305939, #72305986, #72319567, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 6482004);
Finite Group Databasebeta