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Cayley diagramAliases
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 86 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86)
Conjugacy classes & character table
249 conjugacy classes — view the full character table.
Relationships
| center of | C3×D3×C83, H(3,𝔽3)×C83, 3−1+2×C83, … |
| derived subgroup of | D249, Dic249, D3×D83, … |
| Fitting subgroup of | D3×C83, C3×D83, D249, … |
| socle of | D3×C83, C3×D83, D249, … |
| maximal subgroup of | D3×C83, C3×D83, D249, … |
| maximal normal subgroup of | D3×C83, C3×D83, D249, … |
| maximal quotient of | C2×C3×C83, C9×C83, C32×C83, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(249, 1);
Finite Group Databasebeta