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C₂×#20122 #6359454

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

Aliases

Subgroups

1720 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)(10,11)(12,18)(16,17)(19,20)(21,28)(22,26)(23,31)(24,27)(25,30)(29,34)(32,33);(3,4)(5,9)(6,10)(7,11)(8,14)(12,16)(13,17)(15,18)(21,29)(25,33)(28,34)(30,32);(3,5,7,13)(4,9,11,17)(6,12,14,18)(8,15,10,16)(19,21)(20,25)(22,30)(23,32)(24,29)(26,34)(27,33)(28,31);(4,10)(6,14)(8,11)(9,16)(12,18)(15,17)(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, 6266650);