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C₂×#13249 #495238

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

Aliases

Subgroups

1184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402434);