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C₂×#33350 #7622447

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

Aliases

Subgroups

4304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529643);