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C₂×C₂₉×#585 #16817307

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 47 points:

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

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2325);