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C₂×#20972 #6371475

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

Aliases

Subgroups

6910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278671);