Finite Group Databasebeta

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C₂×#13355 #498937

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

Aliases

Subgroups

2157 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406133);