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C₃₁×#3123 #16843056

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 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)(34,37)(35,36)(38,39)(40,41,43,47)(42,49,50,45)(44,46,52,48)(51,54,55,53);(33,36)(37,39)(40,42)(41,45)(43,50)(44,51)(46,53)(47,49)(48,54)(52,55);(41,46)(44,52)(45,53)(47,48)(49,54)(51,55);(32,34,35,38)(33,37,36,39)(42,50)(45,49)(51,55)(53,54)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1855);