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C₂×#33369 #7622477

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

Aliases

Subgroups

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 7529673);