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C₂×#19937 #6358308

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

Aliases

Subgroups

1892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265504);