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C2×C3⋊(C5⋊AGL(1,𝔽11)) #15693172

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

Aliases

direct productC2×C3⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C3)⋊(C5⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C5)⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect product(C2×C11⋊C5)⋊D15
unambiguous semidirect product(C2×D165)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11 ⋊ C2×C5
derivedC3×C5×C11 ⋊ C22×C5
HallC3×C5×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D3
HallC3×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×D15
SylowC3 ⋊ C2×C5⋊AGL(1,𝔽11)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊AGL(1,𝔽11))
commutator, cosocle, hypocenterC3×C5×C11C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11C2×C5
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×C3⋊(C5⋊AGL(1,𝔽11)), C2×C7×C3⋊(C5⋊AGL(1,𝔽11)), C2×C3⋊(C5⋊(C7⋊AGL(1,𝔽11))), …
maximal normal subgroup ofC2×C7×C3⋊(C5⋊AGL(1,𝔽11)), C2×C11×C3⋊(C5⋊AGL(1,𝔽11))
maximal quotient ofD7×C3⋊(C5⋊AGL(1,𝔽11)), C2×C7×C3⋊(C5⋊AGL(1,𝔽11)), C2×C3⋊(C5⋊(C7⋊AGL(1,𝔽11))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 92);