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C₂×#10864 #353657

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

Aliases

Subgroups

2378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260853);