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C₂×#13156 #494932

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

Aliases

Subgroups

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402128);