Finite Group Databasebeta

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C₃₁×#2577 #16842510

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

412 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)(32,33,35,36)(34,38,39,37)(40,41,44,43)(42,46,47,45)(50,54)(53,55);(33,36)(37,38)(42,47)(45,46)(48,49,52,51)(50,53,54,55);(32,33)(34,37)(35,36)(38,39)(40,42)(41,45)(43,46)(44,47)(48,50)(49,53)(51,55)(52,54);(32,34)(33,37)(35,39)(36,38)(40,43,44,41)(42,46,47,45)(48,51,52,49)(50,55,54,53)

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, 1309);