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D3×C5⋊AGL(1,𝔽11) #15693154

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

Aliases

direct productD3×C5⋊AGL(1,𝔽11)
unambiguous semidirect product(C5×D3)⋊AGL(1,𝔽11)
unambiguous semidirect product(D3×C11⋊C5)⋊D5
unambiguous semidirect product(D3×D55)⋊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 ⋊ C2×C5⋊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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×C5⋊AGL(1,𝔽11), D21×C5⋊AGL(1,𝔽11), D3×C5⋊(C7⋊AGL(1,𝔽11)), …
maximal normal subgroup ofD3×C7×C5⋊AGL(1,𝔽11), D3×C11×C5⋊AGL(1,𝔽11), D3×D5×AGL(1,𝔽11)
maximal quotient ofD3×C7×C5⋊AGL(1,𝔽11), D21×C5⋊AGL(1,𝔽11), D3×C5⋊(C7⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 74);