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C₂×#20340 #6369741

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

Aliases

Subgroups

7374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276937);