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C₂×#62902 #10586243

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

Aliases

Subgroups

32192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493439);