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C₂×#61978 #10578769

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

Aliases

Subgroups

6966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485965);