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C₂×#7468 #151759

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

Aliases

Subgroups

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 38 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 58955);