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C₂×#3535 #62722

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

Aliases

Subgroups

3651 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)(13,19)(14,22)(24,26);(4,7)(8,10)(11,12,15,16)(13,20,19,17)(14,18,22,23)(21,26,25,24);(3,4)(5,8)(6,7)(9,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,24)(22,23)(25,26);(3,5)(4,8)(6,9)(7,10)(11,13,15,19)(12,17,16,20)(14,21,22,25)(18,24,23,26);(11,14)(12,18)(13,21)(15,22)(16,23)(17,24)(19,25)(20,26)

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, 55710);