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C₂×#60695 #10575313

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

Aliases

Subgroups

7176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482509);