Finite Group Databasebeta

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#72227372

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

4948 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Polycyclic presentation:

2^8,3^2|f^2=gh,g^2=h,b^a=bf,c^a=ch,c^b=ch,e^a=eh,f^a=fg,f^b=fg,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

156 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, 6, F.7*F.8);;
gap> SetPower(coll, 7, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.6);;
gap> SetConjugate(coll, 3, 1, F.3*F.8);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 5, 1, 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, 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);