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C₂×#12872 #493911

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

Aliases

Subgroups

1082 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)(11,12,15,20,16,22,30,21)(13,17,24,33,25,35,41,34)(14,26,28,19,29,18,27,36)(23,37,39,32,40,31,38,42);(4,7)(8,10)(11,13,16,25)(12,17,22,35)(14,23,29,40)(15,24,30,41)(18,31,26,37)(19,32,36,42)(20,33,21,34)(27,38,28,39);(3,5,6,9)(4,8,7,10)(12,18)(14,27)(15,30)(17,31)(19,20)(21,36)(22,26)(23,38)(24,41)(28,29)(32,33)(34,42)(35,37)(39,40)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401107);