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C₂×#60183 #10574159

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

Aliases

Subgroups

10208 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)(6,10,18,24,19,15,27,23)(7,11,21,26,20,16,28,25)(17,22,31,33,30,29,34,32);(3,5)(4,9)(6,15)(7,16)(8,12)(10,19)(11,20)(13,14)(17,29)(18,23)(21,25)(22,30)(24,27)(26,28)(31,32)(33,34);(3,6,8,18,9,19,14,27)(4,10,13,24,5,15,12,23)(7,17,21,31,20,30,28,34)(11,22,26,33,16,29,25,32);(3,7)(4,11)(5,16)(6,17)(8,21)(9,20)(10,22)(12,25)(13,26)(14,28)(15,29)(18,31)(19,30)(23,32)(24,33)(27,34);(7,20)(11,16)(17,30)(21,28)(22,29)(25,26)(31,34)(32,33)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481355);