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C₂×#22323 #6376753

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

Aliases

Subgroups

1986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6283949);