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C₂×#63052 #10586393

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

Aliases

Subgroups

34580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493589);