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C₂×#12689 #493351

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

Aliases

Subgroups

4120 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)(9,13)(10,17,18,12)(11,14)(15,21,22,19)(16,20);(8,12)(13,19)(14,17)(20,21);(4,6)(7,9,11,16)(8,13,14,20)(10,15,18,22)(12,19,17,21)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400547);