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C₂×#2845 #36689

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

Aliases

Subgroups

871 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29677);