#72248996

order	7040
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₅ · Schur multiplier (H₂) = C₂⁹

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₁₁×#127 ⋊ C₂×C₅
Hall	#13082392 ⋊ C₅
Hall	C₁₁⋊C₅ ⋊ #3498
Sylow	C₁₁ ⋊ C₅×#3498

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×AGL(1,𝔽₁₁)
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵×C₅
Fitting	C₂×C₁₁×#127	C₂×C₅
hypercenter	C₂×#127	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×#3498
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×#127

3496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 352

Polycyclic presentation:

2^5,5,2^2,11|d^2=h,b^a=bg,c^a=cg,d^a=dh,d^b=dh,e^c=eh,i^c=i^10,i^f=i^9

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₁₁)×#3498
maximal normal subgroup of	AGL(1,𝔽₁₁)×#3498

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");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 5, 2, 2, 11]);;
gap> SetPower(coll, 4, F.8);;
gap> SetConjugate(coll, 2, 1, F.2*F.7);;
gap> SetConjugate(coll, 3, 1, F.3*F.7);;
gap> SetConjugate(coll, 4, 1, F.4*F.8);;
gap> SetConjugate(coll, 4, 2, F.4*F.8);;
gap> SetConjugate(coll, 5, 3, F.5*F.8);;
gap> SetConjugate(coll, 9, 3, F.9^10);;
gap> SetConjugate(coll, 9, 6, F.9^9);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);