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C₂×#12886 #494077

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

Aliases

Subgroups

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401273);