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C₂×#14740 #607672

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

Aliases

Subgroups

4942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,6)(11,12,15,16)(13,17,18,14)(19,20,23,22)(21,25,26,24);(8,10)(12,16)(13,18)(19,21,23,26)(20,24,22,25);(7,8)(9,10)(11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,25)(23,26);(3,4)(5,6)(11,14,15,17)(12,13,16,18)(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, 514868);