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C₂×#33956 #7623922

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

Aliases

Subgroups

1308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7531118);