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D15⋊AGL(1,𝔽11) #15693155

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

Aliases

unambiguous semidirect productD15⋊AGL(1,𝔽11)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊D5
unambiguous semidirect product(C5⋊AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D15⋊D11)⋊C5

Splittings

Fitting, socle, derivedC3×C5×C11 ⋊ C22×C5
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D3
HallC3×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C5×D3×D5
SylowC3 ⋊ D5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11C22×C5
LCSG ▷ C3×C5×C11
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 165

Polycyclic presentation:

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

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D15⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽11))⋊D21, (C3⋊AGL(1,𝔽11))⋊D35, …
maximal normal subgroup ofC7×D15⋊AGL(1,𝔽11), C11×D15⋊AGL(1,𝔽11), D3×D5×AGL(1,𝔽11)
maximal quotient ofC7×D15⋊AGL(1,𝔽11), (C5⋊AGL(1,𝔽11))⋊D21, (C3⋊AGL(1,𝔽11))⋊D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 75);