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C₂×#7157 #126655

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

Aliases

Subgroups

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 33851);