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C₂×#62898 #10586238

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

Aliases

Subgroups

34548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493434);