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C₂²×#1909 #6371539

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

Aliases

Subgroups

6114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278735);