Finite Group Databasebeta

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C₂×#12754 #493560

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

Aliases

Subgroups

2492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400756);