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C₂×#13155 #494927

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

Aliases

Subgroups

886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402123);