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C₂×#33421 #7622548

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

Aliases

Subgroups

1670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

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, 7529744);