Finite Group Databasebeta

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C₂×C₂₉×#424 #16816618

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 points:

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

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1636);