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C₂×#408×C₁₀₇ #28333561

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 129 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(3,4)(5,6)(7,8,10,13,11,14,17,20)(9,12,16,19,15,18,21,22);(4,6)(7,9)(8,12)(10,16)(11,15)(13,19)(14,18)(17,21)(20,22);(9,15)(12,18)(16,21)(19,22)

Conjugacy classes & character table

5992 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 1610);