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Cayley diagramAliases
Subgroups
551 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,5,4,6,7,8);(9,10)(11,14)(12,21)(13,15)(16,18)(17,19)(20,22)(23,24);(10,14)(11,18)(12,19)(15,22)(16,17)(20,24)(21,23);(10,15)(14,22)(16,23)(17,21)
Conjugacy classes & character table
128 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | C8×AGL(1,ℤ/16), C2×C8×#509, #72225334, … |
| maximal normal subgroup of | C8×AGL(1,ℤ/16), C2×C8×#509, #72225334, … |
| maximal quotient of | C8×#2177, C2×C8×#509, #72225391, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 390696);
Finite Group Databasebeta