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C₂×#21293 #6372146

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

Aliases

Subgroups

2130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279342);