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C₂×#13051 #494603

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

Aliases

Subgroups

1913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401799);