Finite Group Databasebeta

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#72227366

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(34,35)(36,37);(2,9,11,22)(3,13)(5,20)(8,23,24,25)(10,27,28,18)(12,29,30,26)(14,16)(17,21)(33,34,35);(1,3)(2,8,11,24)(4,16)(5,19)(6,14)(7,13)(9,25,22,23)(10,26,28,29)(12,27,30,18)(15,21)(17,31)(20,32)(37,38);(1,2,4,9,7,11,6,22)(3,12,14,26,13,30,16,29)(5,18,17,28,20,27,21,10)(8,19,23,15,24,32,25,31)

Polycyclic presentation:

2^8,3^2|a^2=e,b^2=eg,c^2=eg,e^2=h,f^2=g,g^2=h,b^a=bf,c^a=cgh,c^b=ch,e^b=eh,f^a=fg,f^b=fg,f^c=fh,g^a=gh,g^b=gh,i^b=i^2,i^d=i^2,j^b=i^2j,j^d=j^2

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 3, 3]);;
gap> SetPower(coll, 1, F.5);;
gap> SetPower(coll, 2, F.5*F.7);;
gap> SetPower(coll, 3, F.5*F.7);;
gap> SetPower(coll, 5, F.8);;
gap> SetPower(coll, 6, F.7);;
gap> SetPower(coll, 7, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.7*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 5, 2, F.5*F.8);;
gap> SetConjugate(coll, 6, 1, F.6*F.7);;
gap> SetConjugate(coll, 6, 2, F.6*F.7);;
gap> SetConjugate(coll, 6, 3, F.6*F.8);;
gap> SetConjugate(coll, 7, 1, F.7*F.8);;
gap> SetConjugate(coll, 7, 2, F.7*F.8);;
gap> SetConjugate(coll, 9, 2, F.9^2);;
gap> SetConjugate(coll, 9, 4, F.9^2);;
gap> SetConjugate(coll, 10, 2, F.9^2*F.10);;
gap> SetConjugate(coll, 10, 4, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);