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C₂×#11912 #483011

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

Aliases

Subgroups

729 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390207);