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C₂×#61061 #10576071

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

Aliases

Subgroups

10390 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)(11,24)(12,15)(13,20)(16,27)(18,33)(19,35)(21,38)(22,34)(23,31)(25,28)(26,32)(29,37)(30,36);(7,9,12,18)(8,13,15,28)(10,21,23,37)(11,25,27,20)(14,30,31,35)(16,33,24,17)(19,26,36,22)(29,34,38,32);(4,6)(9,18)(13,28)(17,33)(19,36)(20,25)(21,37)(29,38)(30,35);(7,10,12,23)(8,14,15,31)(9,19,18,36)(11,26,27,22)(13,29,28,38)(16,34,24,32)(17,35,33,30)(20,37,25,21);(8,15)(13,28)(14,31)(16,24)(17,33)(29,38)(30,35)(32,34)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483267);