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C₂×#34201 #7625500

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

Aliases

Subgroups

11906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532696);