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C₂×#11679 #481338

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

Aliases

Subgroups

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388534);