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C₂×#21734 #6373848

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

Aliases

Subgroups

1902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6281044);