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C₂²×#3028 #10574881

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

Aliases

Subgroups

22154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482077);