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C₂×#36078 #7629580

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

Aliases

Subgroups

23474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536776);