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C₂×#11225 #358018

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

Aliases

Subgroups

1950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 265214);