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C₂×#62938 #10586281

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

Aliases

Subgroups

32462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,9)(5,11)(7,15)(14,17)(21,27)(25,29)(28,33)(32,34);(3,4)(5,10)(6,11)(7,12)(8,9)(13,17)(14,18)(15,16)(19,20,24,23)(21,25,27,29)(22,26,30,31)(28,32,33,34);(3,5)(4,6)(7,13)(8,11)(9,10)(12,14)(15,18)(16,17)(19,21)(20,25)(22,28)(23,29)(24,27)(26,32)(30,33)(31,34);(3,5)(4,10)(6,9)(7,13)(8,11)(12,17)(14,16)(15,18)(19,22)(20,26)(21,28)(23,31)(24,30)(25,32)(27,33)(29,34);(3,6,8,10)(4,11,9,5)(7,14,15,17)(12,18,16,13)(19,23,24,20)(21,29,27,25)(22,26,30,31)(28,32,33,34);(3,7,8,15)(4,12,9,16)(5,13,11,18)(6,14,10,17)(19,21)(20,25)(22,28)(23,29)(24,27)(26,32)(30,33)(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, 10493477);