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C₂×#10786 #353467

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

Aliases

Subgroups

4050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,12,18,13,16,11,17)(9,14,21,28,20,29,26,32)(10,22,24,15,25,31,23,30)(19,33,35,37,34,38,36,27);(4,6)(7,9)(8,14,16,29)(10,19)(11,21)(12,26)(13,20)(15,27,30,37)(17,28,18,32)(22,33,31,38)(23,35)(24,36)(25,34);(7,10,13,25)(8,15,16,30)(9,19,20,34)(11,24,12,23)(14,27,29,37)(17,31,18,22)(21,36,26,35)(28,38,32,33)

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, 260663);