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C₂×#60184 #10574161

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

Aliases

Subgroups

10186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481357);