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C₂×#61078 #10576083

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

Aliases

Subgroups

10450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483279);