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C₂×#63046 #10586372

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

Aliases

Subgroups

32950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493568);