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C₂×#28225 #6465407

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

Aliases

Subgroups

3322 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)(16,20)(17,21)(19,24)(22,26);(7,8,9,10)(11,13,15,21,16,22,24,14)(12,17,19,18,20,23,25,26);(4,6)(8,10);(11,14,24,22,16,21,15,13)(12,18,25,17,20,26,19,23)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6372603);