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C₂×#11682 #481340

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

Aliases

Subgroups

822 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)(13,22,25,38)(14,18)(15,29)(16,21)(17,24,33,42)(19,27)(20,28)(23,36,26,39)(30,32,40,34)(31,35)(37,41);(3,5)(4,7)(6,8)(9,10)(11,13)(12,17)(14,26)(15,30)(16,25)(18,34)(19,36)(20,32)(21,33)(22,35)(23,28)(24,41)(27,42)(29,38)(31,40)(37,39);(4,5)(8,9)(11,14,16,28)(12,18,21,20)(13,23,25,26)(15,27,31,41)(17,32,33,34)(19,35,37,29)(22,36,38,39)(24,40,42,30)

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, 388536);