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C₂×#25799 #6443341

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

Aliases

Subgroups

4994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350537);