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C₂×#24227 #6442558

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

Aliases

Subgroups

4704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349754);