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C₂²×#2133 #7622474

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

Aliases

Subgroups

4190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529670);