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C₃⋊#16864502 #27188552

• 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 113 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)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,69)(41,56,66)(44,59,64)(47,62,61)(50,54,58)(52,67,55)(57,72,84)(60,75,82)(63,78,80)(65,73,77)(68,83,74)(70,85,71)(76,88,95)(79,90,94)(81,89,92)(86,96,87)(91,97,101)(93,98,100)(99,102,103)(105,108,109,106,107,110)(112,113);(1,2,4,8,15,25,38,54,33,12,19,29,42,58,74,87,96,67,35,48,64,80,92,72,37,52,68,69,84,95,101,103,97,75,40,14,23,34,47,63,79,91,98,78,43,17,3,6,11,18,28,41,57,73,46,20,5,9,16,26,39,55,71,83,49,22,32,45,61,77,53,70,86,85,51,66,82,94,100,88,56,24,36,50,65,81,93,99,102,90,59,27,7,13,21,31,44,60,76,89,62,30,10)(104,105,107,110,109,108,106)(111,112,113)

Polycyclic presentation:

2,3^2,7,103|c^a=c^2,d^a=d^6,d^b=d^2,e^b=e^46

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12978, 47);