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C2×C3×C5×AGL(1,𝔽11) #15693167

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

Aliases

direct productC2×C3×C5×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C2×C3×C52)
unambiguous semidirect product(C2×D11)⋊(C3×C52)
unambiguous semidirect product(C11⋊C5)⋊(C22×C3×C5)
unambiguous semidirect product(C2×C11⋊C5)⋊(C2×C3×C5)
unambiguous semidirect product(C2×C3×D11)⋊C52
unambiguous semidirect product(C2×C5×D11)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C5×D11)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11 ⋊ C2×C5
derived, SylowC11 ⋊ C22×C3×C52
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C3
HallC2×C3×D11 ⋊ C52
HallC2×D11 ⋊ C3×C52
HallC3×C11 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5AGL(1,𝔽11)
commutator, cosocle, hypocenterC11C22×C3×C52
FrattiniC1G
Fitting, socleC2×C3×C5×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×AGL(1,𝔽11), C2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×C5×ΓL(1,𝔽8)×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C3×C5×C7×AGL(1,𝔽11), C2×C3×C5×C11×AGL(1,𝔽11)
maximal quotient ofC5×AGL(1,𝔽7)×AGL(1,𝔽11), C2×C5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C2×C5×ΓL(1,𝔽8)×AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 87);