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C₂×#17970 #6344799

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

Aliases

Subgroups

1818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251995);