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C₂×#62115 #10579362

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

Aliases

Subgroups

6468 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)(21,28)(22,26)(23,31)(24,27)(25,30)(29,34)(32,33);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(21,29)(25,33)(28,34)(30,32);(19,21)(20,25)(22,30)(23,32)(24,29)(26,34)(27,33)(28,31);(5,12)(8,11)(13,18)(16,17)(19,22,24,23)(20,26,27,31)(21,30,29,32)(25,34,33,28);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10486558);