Finite Group Databasebeta

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C₂×#10906 #353940

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

Aliases

Subgroups

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,13,9,14,8,12)(5,15,17,10,19,25,18,26)(6,20,22,27,23,28,21,11)(16,30,32,29,33,24,31,34);(3,5,8,18,9,19,7,17)(4,10,13,25,14,26,12,15)(6,16,21,31,23,33,22,32)(11,24,20,34,27,30,28,29);(3,6,7,22,9,23,8,21)(4,11,13,20,14,27,12,28)(5,16,17,32,19,33,18,31)(10,24,25,34,26,30,15,29)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261136);