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C₂×#20131 #6359464

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

Aliases

Subgroups

1828 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266660);