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C₂×#11101 #357682

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

Aliases

Subgroups

3174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264878);