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C₂²×#13309 #72311749

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

12385 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

(6,11)(7,15,17,19)(8,16)(9,21)(12,25,22,27)(13,29)(18,31,33,30)(20,32)(23,26)(28,36,34,35);(1,2);(1,2)(3,4)(5,6)(8,13)(9,14)(10,11)(16,26)(20,23)(21,24)(29,32);(3,4);(1,2)(3,4)(5,7,16,31,21,33,8,19,10,17,32,30,9,18,20,15)(6,12,26,35,24,34,13,25,11,22,29,36,14,28,23,27)

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((6,11)(7,15,17,19)(8,16)(9,21)(12,25,22,27)(13,29)(18,31,33,30)(20,32)(23,26)(28,36,34,35), (1,2), (1,2)(3,4)(5,6)(8,13)(9,14)(10,11)(16,26)(20,23)(21,24)(29,32), (3,4), (1,2)(3,4)(5,7,16,31,21,33,8,19,10,17,32,30,9,18,20,15)(6,12,26,35,24,34,13,25,11,22,29,36,14,28,23,27));