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C₂×#61570 #10577168

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

Aliases

Subgroups

8372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484364);