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C₂×#61669 #10577274

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

Aliases

Subgroups

8022 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)(13,22)(14,19)(15,20)(16,18)(17,23)(21,24)(25,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,16)(15,23)(18,26)(19,21)(20,22)(24,25);(12,18)(13,23)(16,24)(17,19)(20,21)(22,26);(5,10)(7,9)(11,14)(12,19)(13,24)(15,25)(16,23)(17,18)(20,26)(21,22);(4,8)(7,9)(12,20)(13,23)(14,25)(18,21)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484470);