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C₂×#13286 #495380

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

Aliases

Subgroups

874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 42 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402576);