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C₂×#43052 #7667156

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

Aliases

Subgroups

6224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(5,9)(8,10)(11,12)(13,14)(15,16)(17,18)(20,23)(24,25);(3,4)(5,10)(6,7)(8,9)(11,12,15,16)(13,18,17,14)(19,20)(21,25)(22,23)(24,26);(4,7)(8,10)(12,16)(13,17);(3,4)(5,8)(6,7)(9,10)(11,13,15,17)(12,14,16,18)(19,21,22,26)(20,24,23,25);(3,5)(4,8)(6,9)(7,10)(11,14)(12,17)(13,16)(15,18)

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, 7574352);