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C₂×#7998 #181286

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

Aliases

Subgroups

1466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88482);