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C₂×#62788 #10585966

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

Aliases

Subgroups

34550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493162);