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C₂×#13267 #495334

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

Aliases

Subgroups

850 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)(11,12,15,20,16,19,29,32,17,21,30,35,14,28,23,38)(13,22,26,37,27,33,40,41,24,36,39,42,25,18,31,34);(4,7)(8,9)(11,13,23,31,14,25,30,39,17,24,29,40,16,27,15,26)(12,18,32,37,28,36,20,34,21,33,38,42,19,22,35,41);(3,5,6,10)(4,8,7,9)(13,24)(18,33)(22,36)(25,27)(26,39)(31,40)(34,41)(37,42)

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, 402530);