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C₂²×#2117 #7622436

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

Aliases

Subgroups

4066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529632);