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C₂×#19778 #6358118

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

Aliases

Subgroups

1727 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265314);