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C2×C5×C3⋊AGL(1,𝔽11) #15693170

order3300
isoclinismisoclinic class of C3⋊AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×C3⋊AGL(1,𝔽11)
unambiguous semidirect product(C2×C3)⋊(C5×AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊(C5×D3)
unambiguous semidirect product(C2×D33)⋊C52
unambiguous semidirect product(C2×C5×D33)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C52
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D3
HallC2×D33 ⋊ C52
SylowC11 ⋊ C2×C52×D3
SylowC3 ⋊ C2×C5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊AGL(1,𝔽11)
commutator, cosocle, hypocenterC3×C11C22×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C11C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D7×C3⋊AGL(1,𝔽11), C2×C5×C7×C3⋊AGL(1,𝔽11), C2×C5×C3⋊(C7⋊AGL(1,𝔽11)), …
maximal normal subgroup ofC2×C5×C7×C3⋊AGL(1,𝔽11), C2×C5×C11×C3⋊AGL(1,𝔽11)
maximal quotient ofC5×D7×C3⋊AGL(1,𝔽11), C2×C5×C7×C3⋊AGL(1,𝔽11), C2×C5×C3⋊(C7⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 90);