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C₂×#33701 #7623164

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

Aliases

Subgroups

1694 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)(13,26)(14,19)(15,21)(16,35)(17,37)(18,25)(20,29)(22,33)(23,36)(24,34)(27,39)(28,40)(30,38)(31,42)(32,41);(4,7)(8,10)(11,13,17,28,15,27,16,14,18,29,33,30,34,31,36,32)(12,19,23,39,24,40,22,26,25,41,35,42,21,38,37,20);(3,5,6,9)(4,8,7,10)(11,14,16,31,34,28,17,29,18,32,36,27,15,30,33,13)(12,20,22,40,21,42,23,19,25,26,37,38,24,39,35,41);(11,15,18,34)(12,21,25,24)(13,27,29,31)(14,30,32,28)(16,33,36,17)(19,38,41,40)(20,42,26,39)(22,23,37,35)

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, 7530360);