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C₂×#46570 #7700145

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

Aliases

Subgroups

6186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7607341);