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C₂×#13012 #494493

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

Aliases

Subgroups

1682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401689);