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C₂×#13162 #495010

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

Aliases

Subgroups

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402206);