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C₂×#62134 #10579382

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

Aliases

Subgroups

6420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486578);