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C₂×#35794 #7629202

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

Aliases

Subgroups

6236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536398);