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#72247347

order3960
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C2×C3

Aliases

No aliases for this group.

Splittings

Fitting, socleC22×C3×C11 ⋊ C5×D3
derivedC3×C11×A4 ⋊ C2×C5
HallC3⋊(C11⋊S4) ⋊ C5
HallC11⋊C5 ⋊ C3⋊S4
SylowC11 ⋊ C5×C3⋊S4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C11×A4C2×C5
Fitting, socleC22×C3×C11C5×D3
LCSG ▷ C3×C11×A4
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 132

Polycyclic presentation:

2,5,3^2,11,2^2|c^a=c^2,d^a=d^2,e^a=e^10,e^b=e^5,f^a=fg,f^c=g,g^c=fg

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofS4×C3⋊AGL(1,𝔽11), D3×A4⋊AGL(1,𝔽11), C3⋊S4×AGL(1,𝔽11), …
maximal normal subgroup ofS4×C3⋊AGL(1,𝔽11), D3×A4⋊AGL(1,𝔽11), C3⋊S4×AGL(1,𝔽11)
maximal quotient of#72268737

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