Finite Group Databasebeta

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C₂×#12781 #493623

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

Aliases

Subgroups

2432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400819);