Finite Group Databasebeta

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C₄₇×#542 #15688797

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 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)(50,54)(51,53)(52,55)(58,62)(60,63);(48,49,51,53)(50,52,55,54)(56,57,59,61)(58,60,62,63);(48,49)(50,52)(51,53)(54,55)(56,58)(57,60)(59,62)(61,63);(48,50,51,55)(49,52,53,54)

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 223);