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C₂²×#2098 #6432427

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

Aliases

Subgroups

3198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339623);