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C₂×#13490 #499367

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

Aliases

Subgroups

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406563);