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C₂×#24278 #6442575

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

Aliases

Subgroups

5060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349771);