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C₂×#13154 #494926

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

Aliases

Subgroups

778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402122);