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C₂×#35766 #7629320

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

Aliases

Subgroups

6770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536516);