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C₂×#24377 #6437656

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

Aliases

Subgroups

4962 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)(13,20)(17,25)(21,26)(22,23);(4,6)(11,12,15,19)(13,21,20,26)(14,18,16,24)(17,22,25,23);(8,10)(11,13,15,20)(12,17,19,25)(14,23,16,22)(18,26,24,21);(4,6)(11,14,15,16)(12,18,19,24)(13,22,20,23)(17,21,25,26)

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, 6344852);