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C₂×#21737 #6373849

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

Aliases

Subgroups

1858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

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

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, 6281045);