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C₂²×#2049 #6431931

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

Aliases

Subgroups

4598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339127);