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C₂×#61707 #10577875

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

Aliases

Subgroups

7748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10485071);