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C₂×#35838 #7629212

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

Aliases

Subgroups

5778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536408);