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C3⋊(C3⋊(C11⋊AGL(1,𝔽5))) #14520453

order1980
isoclinismisoclinic class of C3⋊(C3⋊(C11⋊AGL(1,𝔽5)))
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊(C11⋊AGL(1,𝔽5)))
unambiguous semidirect productC11⋊(C3⋊ΓL(1,𝔽16))

Splittings

Fitting, socle, derived, HallC32×C5×C11 ⋊ C4
HallC32×C11 ⋊ AGL(1,𝔽5)
HallC5×C11 ⋊ C3⋊Dic3
HallC32×C5 ⋊ Dic11
SylowC11 ⋊ C3⋊ΓL(1,𝔽16)
SylowC32 ⋊ C11⋊AGL(1,𝔽5)
SylowC5 ⋊ C3⋊Dic33

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C5×C11C4
prime radical, cosocleC32×D5×C11C2
LCSG ▷ C32×C5×C11
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 495

Polycyclic presentation:

2^2,3^2,5,11|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^10,e^b=e^4

Conjugacy classes & character table

201 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), C3⋊(C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))), C3⋊(C3⋊(C121⋊AGL(1,𝔽5))), …
maximal normal subgroup ofC7×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), C11×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), C13×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), …
maximal quotient ofC7×C3⋊(C3⋊(C11⋊AGL(1,𝔽5))), C3⋊(C3⋊(C7⋊(C11⋊AGL(1,𝔽5)))), C3⋊(C3⋊(C121⋊AGL(1,𝔽5))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 78);