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C₂²×#2053 #6431947

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

Aliases

Subgroups

4722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339143);