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C₂×#3518 #62791

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

Aliases

Subgroups

3559 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55779);