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C₂×#33702 #7623165

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

Aliases

Subgroups

1734 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)(12,18)(13,23)(14,15)(16,27)(20,31)(21,32)(22,36)(24,25)(26,38)(28,29)(30,34)(35,41)(37,39)(40,42);(4,7)(8,10)(11,12,15,21,16,22,28,31,17,20,29,36,27,32,14,18)(13,19,23,34,25,35,37,40,26,33,38,42,39,41,24,30);(3,5,6,9)(4,8,7,10)(11,13,14,24,27,39,29,38,17,26,28,37,16,25,15,23)(12,19,18,30,32,41,36,42,20,33,31,40,22,35,21,34);(12,20)(18,31)(19,33)(21,36)(22,32)(30,40)(34,42)(35,41)

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, 7530361);