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C₂²×#2103 #6432447

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

Aliases

Subgroups

1930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339643);