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C₂×#20673 #6370826

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

Aliases

Subgroups

4502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278022);