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C₂²×#2957 #10574146

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

Aliases

Subgroups

10322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481342);