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C₂×#34174 #7625430

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

Aliases

Subgroups

24258 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)(12,13)(15,23)(17,19)(21,26);(11,12,16,13)(14,19,22,17)(15,18,23,20)(21,25,26,24);(3,4)(5,6)(7,8)(9,10)(11,13,16,12)(14,19,22,17)(15,20,23,18)(21,25,26,24);(11,14,16,22)(12,17,13,19)(15,21,23,26)(18,24,20,25);(11,15)(12,18)(13,20)(14,21)(16,23)(17,24)(19,25)(22,26)

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, 7532626);