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C₂×#7111 #124065

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

Aliases

Subgroups

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 42 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 31261);