Finite Group Databasebeta

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C₃₁×#3486 #16843419

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(33,35)(37,41)(39,47)(42,44)(45,51);(36,37,40,41)(38,44,46,42)(39,43,47,48)(45,50,51,49);(32,33)(34,35);(36,38,40,46)(37,42,41,44)(39,45,47,51)(43,49,48,50);(36,39)(37,43)(38,45)(40,47)(41,48)(42,49)(44,50)(46,51)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2218);