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C₂×#13448 #499165

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

Aliases

Subgroups

1292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406361);