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C₂×#3538 #62725

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

Aliases

Subgroups

3581 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55713);