Finite Group Databasebeta

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C₃₁×#2591 #16842524

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

596 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)(38,40)(39,42)(41,43)(45,48)(46,50);(37,38)(41,42)(44,45,47,48)(46,49,50,51);(32,33)(34,35)(36,38,40,37)(39,42,43,41);(36,39)(37,41)(38,42)(40,43)(44,46)(45,49)(47,50)(48,51)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1323);