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C₂×#20633 #6370772

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

Aliases

Subgroups

5874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6277968);