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Cayley diagramAliases
Subgroups
3048 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 24 points:
(1,2,3,4);(5,6)(7,8)(10,14)(12,15)(16,20)(17,21)(19,22)(23,24);(9,10,15,21,13,17,12,14)(11,16,22,24,18,23,19,20);(6,8)(9,11)(10,16)(12,19)(13,18)(14,20)(15,22)(17,23)(21,24);(11,18)(16,23)(19,22)(20,24)
Conjugacy classes & character table
128 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | AGL(1,𝔽5)×#3058, C4×#60698, #72320128, … |
| maximal normal subgroup of | C4×#60698, #72320128, #72321418, … |
| maximal quotient of | AGL(1,𝔽5)×#3058, #72320225, C4×#24267 |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(512, 6280148);
Finite Group Databasebeta