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C₂×#20392 #6369815

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

Aliases

Subgroups

6354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277011);