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C₂×#33766 #7623299

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

Aliases

Subgroups

1686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530495);