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C₂×#13014 #494494

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

Aliases

Subgroups

1574 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)(11,12,14,20,24,26,23,17,16,22,13,19,15,21,25,18);(3,4,5,6)(12,17)(13,23)(14,25)(15,24)(18,22)(19,21)(20,26);(8,10)(12,18)(13,23)(14,25)(15,24)(17,22)(19,26)(20,21)

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, 401690);