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C₂×#33434 #7622571

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

Aliases

Subgroups

2030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529767);