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C₂×#3127 #60556

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

Aliases

Subgroups

997 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)(11,12,15,19)(13,21,23,17)(14,25,26,34)(16,29,28,20)(18,30,33,27)(22,37,38,42)(24,32,40,36)(31,39,35,41);(4,7)(8,10)(11,13)(12,17)(14,22)(15,23)(16,24)(18,31)(19,21)(20,32)(25,42)(26,38)(27,39)(28,40)(29,36)(30,41)(33,35)(34,37);(11,14,15,26)(12,18,19,33)(13,22,23,38)(16,30,28,27)(17,31,21,35)(20,34,29,25)(24,41,40,39)(32,37,36,42);(3,5,6,9)(4,8,7,10)(13,23)(17,21)(22,38)(24,40)(31,35)(32,36)(37,42)(39,41)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53544);