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C₂×#11401 #479901

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

Aliases

Subgroups

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387097);