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C₂×#35964 #7629274

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

Aliases

Subgroups

6054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(11,12,15,14)(13,17,18,16)(19,20,23,26)(21,22,25,24);(3,4)(5,8)(6,9)(7,10)(19,21,23,25)(20,24,26,22);(3,5)(4,7)(6,10)(8,9)(11,13,15,18)(12,16,14,17)(19,20)(21,24)(22,25)(23,26);(3,5)(4,8)(6,10)(7,9)(11,14,15,12)(13,17,18,16)(19,22,23,24)(20,25,26,21);(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, 7536470);