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C₂²×#2143 #7622501

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

Aliases

Subgroups

4066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529697);