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C₂×#62833 #10586182

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

Aliases

Subgroups

34398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493378);