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C₂×#8492 #187391

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

Aliases

Subgroups

2230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94587);