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C₂×#62235 #10579488

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

Aliases

Subgroups

6396 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)(21,25)(22,28)(23,27)(24,29)(26,30)(31,34)(32,33);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,17)(15,18)(19,21)(20,25)(22,32)(23,30)(24,31)(26,27)(28,33)(29,34);(19,21)(20,26)(22,30)(23,32)(24,31)(25,27)(28,34)(29,33);(5,12)(8,11)(13,18)(16,17)(19,22,24,23)(20,27,29,28)(21,30,31,32)(25,33,34,26);(3,6,7,15)(4,9,10,14)(5,13,12,18)(8,16,11,17)(19,22,24,23)(20,28,29,27)(21,30,31,32)(25,26,34,33)

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, 10486684);