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C₃⋊#20259718 #32914901

• 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:

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

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 64);