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C₂×#24783 #6442880

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

Aliases

Subgroups

2956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350076);