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C₂×#33881 #7623685

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

Aliases

Subgroups

1628 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)(13,17,22,32)(14,18,27,35)(15,28,26,20)(19,36,34,25)(23,33,37,29)(24,41,38,31)(30,39,42,40);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,23)(15,24)(16,22)(18,33)(19,30)(20,31)(21,32)(25,40)(26,38)(27,37)(28,41)(29,35)(34,42)(36,39);(12,18)(13,22)(14,25)(15,26)(17,29)(19,20)(21,35)(23,39)(27,36)(28,34)(30,41)(31,42)(32,33)(37,40);(5,10)(7,9)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530881);