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C₂×#2744 #52180

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

Aliases

Subgroups

1035 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45168);