Finite Group Databasebeta

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C₂×#12779 #493618

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

Aliases

Subgroups

2349 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400814);