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C₂×#32951 #6629048

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

Aliases

Subgroups

4486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6536244);