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C₂×#21233 #6371995

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

Aliases

Subgroups

6306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279191);