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C₂×#20618 #6370745

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

Aliases

Subgroups

17294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6277941);