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C₂×#13545 #499561

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

Aliases

Subgroups

494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406757);