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C₂×#3495 #62803

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

Aliases

Subgroups

3603 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55791);