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C₂×#12641 #493059

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

Aliases

Subgroups

1178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400255);