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C₂×#60034 #7665998

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

Aliases

Subgroups

7916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573194);