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C₂×#6157 #88333

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 55 points:

(4,5,6,8)(7,10,11,17)(9,14,15,13)(12,19,20,30)(16,23,24,26)(18,27,28,22)(21,32,33,45)(25,36,37,42)(29,34,40,39)(31,43,44,35)(38,46,47,52)(41,48,49,51)(50,53,54,55);(1,2)(3,4,7,12,21,34,23,10,18,29,41,50,53,46,32,44,30,42,51,47,37,24,15,8,13,22,35,43,27,14,5,9,16,25,38,48,36,19,31,45,52,55,54,49,40,28,17,26,39,33,20,11,6)

Conjugacy classes & character table

34 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(424, 12);