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C₂×#61054 #10576064

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

Aliases

Subgroups

10498 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)(9,18)(10,15)(11,16)(12,25)(13,17)(14,19)(20,35)(21,28)(22,31)(23,38)(24,33)(26,30)(27,34)(29,36)(32,37);(7,9,13,21)(8,14,17,30)(10,19,12,26)(11,23,24,36)(15,28,25,18)(16,32,33,35)(20,27,37,22)(29,31,38,34);(4,6)(7,10,13,12)(8,15,17,25)(9,19,21,26)(11,22,24,27)(14,28,30,18)(16,31,33,34)(20,36,37,23)(29,32,38,35);(7,11,13,24)(8,16,17,33)(9,20,21,37)(10,22,12,27)(14,29,30,38)(15,31,25,34)(18,35,28,32)(19,36,26,23);(8,17)(14,30)(15,25)(16,33)(18,28)(29,38)(31,34)(32,35)

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, 10483260);