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C₂×#62431 #10579197

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

Aliases

Subgroups

7618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486393);