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C₂×#19963 #6358337

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

Aliases

Subgroups

1718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265533);