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C₂×C₄×#368 #493149

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

Aliases

Subgroups

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400345);