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C₂×#13138 #494876

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

Aliases

Subgroups

898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402072);