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C₂×#20232 #6359586

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

Aliases

Subgroups

1601 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,8)(6,14)(9,15)(10,17)(11,18)(12,16)(19,20)(21,28)(22,26)(23,31)(24,27)(25,30)(29,34)(32,33);(3,4,7,9)(5,11,13,17)(6,15,14,8)(10,16,18,12)(21,29)(25,33)(28,34)(30,32);(4,9)(8,15)(10,18)(11,17)(19,21)(20,25)(22,30)(23,32)(24,29)(26,34)(27,33)(28,31);(3,5,7,13)(4,10,9,18)(6,16,14,12)(8,17,15,11)(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, 6266782);