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C₂×#33864 #7623674

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

Aliases

Subgroups

1654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530870);