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C₂×#34172 #7625418

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

Aliases

Subgroups

24690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532614);