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C₂²×#33329 #72239281

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

Aliases

Subgroups

17105 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 36 points:

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

Conjugacy classes & character table

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

Relationships

GAP

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

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