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C₂×#50255 #7705746

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

Aliases

Subgroups

6116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612942);