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C₂×#20623 #6370754

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

Aliases

Subgroups

17158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277950);