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C₂×#3550 #62758

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

Aliases

Subgroups

3537 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55746);