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C₂×#3544 #62749

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

Aliases

Subgroups

3543 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55737);