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C₂×#12574 #492884

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

Aliases

Subgroups

3262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400080);