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C₂×#12714 #493409

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

Aliases

Subgroups

3380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400605);