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C₂×#61454 #10576830

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

Aliases

Subgroups

6988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484026);