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C₂×#20668 #6370820

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

Aliases

Subgroups

4594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278016);