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C₂²×#2155 #7622526

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

Aliases

Subgroups

1962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529722);