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C₂×#11989 #483232

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

Aliases

Subgroups

751 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390428);