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C₂×#3515 #62779

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

Aliases

Subgroups

3571 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55767);