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C₂×#3545 #62753

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

Aliases

Subgroups

3715 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)(13,19)(14,16)(15,22)(17,20)(18,23)(21,24)(25,26);(4,7)(8,10)(12,14)(13,20)(18,22)(21,26);(3,4,6,7)(5,8,9,10)(11,13)(12,17)(14,19)(15,21)(16,20)(18,24)(22,25)(23,26);(3,5)(4,8)(6,9)(7,10)(11,14,16,12)(13,19,20,17)(15,22,23,18)(21,25,26,24);(11,15)(12,18)(13,21)(14,22)(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, 55741);