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C₂×#20738 #6370969

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

Aliases

Subgroups

6498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278165);