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C₂×#43166 #7667358

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

Aliases

Subgroups

6192 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)(15,17)(16,18)(19,20)(21,24)(22,23)(25,26);(3,4)(5,10)(6,7)(8,9)(11,13,16,15)(12,17,18,14)(20,22)(21,25);(4,7)(8,10)(19,20,23,22)(21,26,25,24);(3,4)(5,8)(6,7)(9,10)(11,14,16,17)(12,13,18,15)(19,21,23,25)(20,24,22,26);(3,5)(4,8)(6,9)(7,10)(11,15,16,13)(12,17,18,14)(19,22,23,20)(21,26,25,24)

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, 7574554);