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C₂×#62897 #10586237

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

Aliases

Subgroups

34504 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)(13,21)(14,15)(16,18)(17,20)(19,26)(22,23)(24,25);(11,13,17,16)(12,18,20,21)(14,24,19,22)(15,23,26,25);(3,4)(5,8)(6,7)(9,10)(11,14,17,19)(12,15,20,26)(13,22,16,24)(18,25,21,23);(5,9)(8,10)(11,15)(12,19)(13,23)(14,20)(16,25)(17,26)(18,22)(21,24);(3,5)(4,8)(6,9)(7,10)(11,16,17,13)(12,18,20,21)(14,24,19,22)(15,25,26,23);(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, 10493433);