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C₂×#13196 #495099

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

Aliases

Subgroups

1158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402295);