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C₂×#23547 #6431963

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

Aliases

Subgroups

4998 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)(14,15)(16,20)(17,19)(18,23)(22,24)(25,26);(7,8)(9,10)(11,13,17,25)(12,18,19,22)(14,21,20,26)(15,24,16,23);(4,6)(8,10)(11,14,15,12,17,20,16,19)(13,22,23,26,25,18,24,21);(12,19)(14,20)(18,22)(21,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339159);