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C₂×#7172 #126772

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

Aliases

Subgroups

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2);(3,4,6,9,7,10,5,8)(11,12,15,20,17,23,29,22)(13,24,26,38,28,39,40,33)(14,21,16,19,30,36,31,37)(18,27,32,41,35,42,34,25);(4,8,10,9)(11,13,16,27,15,26,30,41,17,28,31,42,29,40,14,25)(12,18,21,33,22,34,37,39,23,35,36,38,20,32,19,24)

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, 33968);