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C₂×#33435 #7622572

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

Aliases

Subgroups

1986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529768);