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C₂×#19996 #6358388

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

Aliases

Subgroups

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265584);