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C₂×#33742 #7623235

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

Aliases

Subgroups

1404 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)(13,21)(14,25)(15,26)(17,28)(19,34)(20,33)(22,27)(23,38)(24,37)(29,32)(30,39)(31,42)(35,36)(40,41);(4,7)(8,10)(11,12)(13,17)(14,19)(15,20)(16,18)(21,28)(22,29)(23,31)(24,30)(25,34)(26,33)(27,32)(35,40)(36,41)(37,39)(38,42);(11,13,22,38,15,23,14,21,16,24,25,36,26,35,27,37)(12,17,29,42,20,31,19,28,18,30,34,41,33,40,32,39);(3,5,6,9)(4,8,7,10)(12,18)(17,30)(19,32)(20,33)(28,39)(29,34)(31,40)(41,42)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530431);