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C₂×#12724 #493449

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

Aliases

Subgroups

2170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400645);