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C₂×#28180 #6462903

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

Aliases

Subgroups

2388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370099);