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C₂×#11233 #358042

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

Aliases

Subgroups

2010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265238);