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C₂×#23406 #6431729

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

Aliases

Subgroups

7434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6338925);