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C₂²×#3069 #10574894

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

Aliases

Subgroups

10262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482090);