Finite Group Databasebeta

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C₂×#13353 #498936

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

Aliases

Subgroups

2205 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,14)(6,18)(7,10)(8,13)(9,15)(11,21)(12,22)(16,29)(17,27)(19,24)(20,28)(23,33)(25,31)(26,34)(30,32);(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, 406132);