Finite Group Databasebeta

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C₃₁×#3485 #16843418

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1560 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)(36,37)(38,44)(39,47)(40,41)(42,46)(43,48)(45,49)(50,51);(37,41)(42,44)(43,47)(49,50);(32,33)(34,35)(36,38,40,46)(37,42,41,44)(39,45,48,51)(43,49,47,50);(36,37)(38,42)(39,43)(40,41)(44,46)(45,49)(47,48)(50,51);(36,39)(37,43)(38,45)(40,48)(41,47)(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, 2217);