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C₂²×#1902 #6371517

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

Aliases

Subgroups

6034 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)(8,20,23,30)(9,24)(10,14)(11,15)(12,18)(13,22,29,21)(17,32,34,26)(19,27)(25,28)(31,33,36,35);(5,7,9,18,11,19,10,25)(6,12,14,16,15,28,24,27)(8,17,22,35,23,34,21,33)(13,26,30,31,29,32,20,36);(5,8)(6,13)(7,17)(9,22)(10,21)(11,23)(12,26)(14,30)(15,29)(16,31)(18,35)(19,34)(20,24)(25,33)(27,36)(28,32)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278713);