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C₂×#11991 #483238

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

Aliases

Subgroups

719 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,6,12,19,9,18,22,8,13,21,28,7,11,20,27)(5,14,16,29,31,25,32,33,15,26,30,34,17,10,23,24);(4,9)(6,18)(7,19)(10,14)(11,13)(12,28)(16,32)(17,31)(20,21)(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)(19,31)(20,23)(21,30)(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, 390434);