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C₂×#21663 #6373526

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

Aliases

Subgroups

2086 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)(11,12,16,23,18,24,17,22)(13,25,28,19,30,38,29,39)(14,31,15,21,34,40,33,20)(26,36,27,42,32,37,35,41);(4,7)(8,10)(11,13,17,29,18,30,16,28)(12,19,23,38,24,39,22,25)(14,32,33,27,34,26,15,35)(20,37,31,41,21,36,40,42);(3,5,6,9)(4,8,7,10)(11,14,16,15,18,34,17,33)(12,20,22,40,24,21,23,31)(13,26,28,27,30,32,29,35)(19,36,25,41,39,37,38,42);(11,15,16,34,18,33,17,14)(12,21,23,40,24,20,22,31)(13,27,28,32,30,35,29,26)(19,37,38,41,39,36,25,42)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280722);