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Cayley diagramAliases
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 124 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124)
Conjugacy classes & character table
363 conjugacy classes. The character table is too large to display.
Relationships
| center of | C3×D3×C121, C3×D5×C121, C3×D19×C121, … |
| derived subgroup of | D363, Dic363, D3×D121, … |
| Frattini subgroup of | C2×D11979 |
| Fitting subgroup of | D3×C121, C3×D121, D363, … |
| maximal subgroup of | D3×C121, C3×D121, D363, … |
| maximal normal subgroup of | D3×C121, C3×D121, D363, … |
| maximal quotient of | C2×C3×C121, C9×C121, C32×C121, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(363, 1);
Finite Group Databasebeta