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C₂×#55505 #8102472

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

Aliases

Subgroups

6196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009668);