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C₂×#61688 #10577294

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

Aliases

Subgroups

8184 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)(13,19)(14,22)(15,21)(16,20)(17,24)(18,23)(25,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,25)(15,24)(16,23)(18,22)(19,21)(20,26);(11,13)(12,18)(14,23)(15,24)(16,25)(17,22)(19,20)(21,26);(5,10)(7,9)(11,13)(12,19)(14,25)(15,24)(16,23)(17,21)(18,20)(22,26);(4,8)(7,9)(11,14,15,16)(12,20,21,22)(13,23,24,25)(17,18,19,26)

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, 10484490);