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C₂×#13002 #494467

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

Aliases

Subgroups

1496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401663);