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C₂×#23545 #6431955

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

Aliases

Subgroups

4842 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)(13,18)(14,23)(15,25)(16,19)(17,21)(20,24)(22,26);(7,8)(9,10)(11,13,16,22)(12,17,19,23)(14,24,21,15)(18,20,26,25);(4,6)(8,10)(11,14,15,13,16,21,24,22)(12,18,20,23,19,26,25,17);(12,19)(17,23)(18,26)(20,25)

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, 6339151);