Finite Group Databasebeta

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C₄₇×#529 #15688784

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49)(50,53)(51,52)(54,55)(56,57)(58,60)(59,61)(62,63);(49,52)(53,55)(56,58,59,62)(57,60,61,63);(57,61)(60,63);(48,50,51,54)(49,53,52,55)

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 210);