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Cayley diagramAliases
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 1 generator on 109 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)
Conjugacy classes & character table
214 conjugacy classes — view the full character table.
Relationships
| center of | D4×C107, Q8×C107, Dic3×C107, … |
| derived subgroup of | Dic214, D428, C22⋊D107, … |
| Fitting subgroup of | Dic107, C2×D107, Dic107⋊C53, … |
| socle of | Dic107, C4×C107, C2×D107, … |
| maximal subgroup of | Dic107, C4×C107, C2×D107, … |
| maximal normal subgroup of | Dic107, C4×C107, C2×D107, … |
| maximal quotient of | C4×C107, C22×C107, D3×C107, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(214, 2);
Finite Group Databasebeta