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C₂×#11019 #357576

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

Aliases

Subgroups

4590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264772);