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C₂×#60471 #10574911

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

Aliases

Subgroups

10292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482107);