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C₂×#33460 #7622610

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529806);