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C₂×#62965 #10586310

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

Aliases

Subgroups

32500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493506);