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C₂²×#2009 #6431737

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

Aliases

Subgroups

7146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338933);