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C₂×#13553 #512550

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

Aliases

Subgroups

902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419746);