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C₂×#12002 #483324

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

Aliases

Subgroups

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390520);