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C₂×#20229 #6359583

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

Aliases

Subgroups

1591 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266779);