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C₂×#24286 #6442736

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

Aliases

Subgroups

4538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349932);