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C₂×#13003 #494470

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

Aliases

Subgroups

1446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401666);