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C₂×#20071 #6359398

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

Aliases

Subgroups

1834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,10)(5,8,6,9)(11,12,16,14)(13,19,23,26)(15,24,25,18)(17,21,20,22);(3,5,7,6)(4,8,10,9)(11,13,16,23)(12,17,14,20)(15,21,25,22)(18,26,24,19);(4,9)(5,6)(8,10)(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, 6266594);