Finite Group Databasebeta

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C₃₁×#3273 #16843206

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 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)(36,37,40,43)(38,44,45,51)(39,48,49,42)(41,46,50,47);(36,38)(37,41)(39,46)(40,45)(42,51)(43,50)(44,48)(47,49);(33,35)(38,45)(41,50)(44,51)(46,47);(38,46)(39,49)(41,51)(42,48)(44,50)(45,47)

Conjugacy classes & character table

899 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2005);