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C3⋊(C3⋊AGL(1,𝔽11)) #11758368

order990
isoclinismisoclinic class of C3⋊(C3⋊AGL(1,𝔽11))
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊(C3⋊D3)
unambiguous semidirect product(C3⋊D33)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11 ⋊ C2×C5
HallC32×C11⋊C5 ⋊ C2
HallC3⋊D33 ⋊ C5
HallC11⋊C5 ⋊ C3⋊D3
SylowC11 ⋊ C5×C3⋊D3
SylowC32 ⋊ AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11C2×C5
LCSG ▷ C32×C11
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 99

Polycyclic presentation:

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

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊D3×AGL(1,𝔽11), D3×C3⋊AGL(1,𝔽11), C2×C3⋊(C3⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC3⋊D3×AGL(1,𝔽11), D3×C3⋊AGL(1,𝔽11), C2×C3⋊(C3⋊AGL(1,𝔽11)), …
maximal quotient ofC3⋊(C3⋊(Dic11⋊C5)), C2×C3⋊(C3⋊AGL(1,𝔽11)), C3⋊(C3⋊(D121⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(990, 17);