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C₂×#21735 #6373845

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

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, 6281041);