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C₂×#33682 #7623089

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530285);