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C₂×#7177 #126782

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

Aliases

Subgroups

554 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)(11,12,15,20,17,23,34,22)(13,24,26,37,29,39,28,42)(14,30,32,19,33,21,16,35)(18,27,36,25,38,41,40,31);(4,8,10,9)(11,13,16,27,34,26,33,25,17,29,32,41,15,28,14,31)(12,18,21,37,20,40,35,24,23,38,30,42,22,36,19,39)

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, 33978);