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C₂×#7140 #126556

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

Aliases

Subgroups

566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 33752);