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C₃⋊#20259721 #32914898

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 95 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,63)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,67,68,49,50,78)(34,66,51,52,48,60)(37,42,65,54,55,61)(40,74,73,58,59,57)(53,79,71,70,69,76)(56,64,75,72,62,77)(81,85,86,82,83,87)(84,91,90,88,89,92)(94,95);(1,2,5,11,19,32,51,28,43,44,27,42,62,31,48,59,61,63,76,70,52,33,20,4,8,13,23,37,56,73,45,15,26,14,25,40,50,69,68,75,77,78,79,67,58,36,10,16,24,38,57,72,54,35,22,7,6,12,21,34,53,71,47,65,74,66,46,64,55,18,29,39,41,60,49,30,17,9,3)(80,81,84,83,87,90,89,91,92,86,85,88,82)(93,94,95)

Polycyclic presentation:

2,3^2,13,79|c^a=c^2,d^a=d^12,e^a=e^78,d^b=d^3,e^b=e^23

Conjugacy classes & character table

522 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 61);