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C3×D5×AGL(1,𝔽11) #15693148

order3300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×AGL(1,𝔽11)
unambiguous semidirect productD11⋊(C3×C5×D5)
unambiguous semidirect product(D5×D11)⋊(C3×C5)
unambiguous semidirect product(C5×AGL(1,𝔽11))⋊(C2×C3)
unambiguous semidirect product(D5×C11⋊C5)⋊(C2×C3)
unambiguous semidirect product(C5⋊AGL(1,𝔽11))⋊(C2×C3)
unambiguous semidirect product(C3×D5×D11)⋊C5

Splittings

Fitting, socleC3×C5×C11 ⋊ C22×C5
derivedC5×C11 ⋊ C22×C3×C5
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C3
HallC3×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC3D5×AGL(1,𝔽11)
commutator, cosocle, hypocenterC5×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11C22×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 165

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), …
maximal normal subgroup ofC3×C7×D5×AGL(1,𝔽11), C3×D5×C11×AGL(1,𝔽11), C3×AGL(1,𝔽5)×AGL(1,𝔽11), …
maximal quotient ofAGL(1,𝔽11)×C5⋊AGL(1,𝔽7), D5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 68);