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C₂×#63016 #10586335

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

Aliases

Subgroups

34468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493531);