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C₂×#60368 #10574825

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

Aliases

Subgroups

21966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 38 points:

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

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, 10482021);