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C₂×#59272 #7666220

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

Aliases

Subgroups

7616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573416);