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C₃²×#89137 #16841016

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 115 points:

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

Conjugacy classes & character table

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

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3924, 43);