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C₂×#24225 #6442554

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

Aliases

Subgroups

4652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349750);