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C₂×#20027 #6359351

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

Aliases

Subgroups

2002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266547);