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C₂×#11175 #357896

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

Aliases

Subgroups

2746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265092);