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C₂×#60455 #10574906

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

Aliases

Subgroups

10414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10482102);