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C₂×#60076 #10574058

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

Aliases

Subgroups

22390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481254);