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D3×C49×C11⋊C5 #30633478

order16170
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productD3×C49×C11⋊C5
unambiguous semidirect productC3⋊(C2×C49×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C5×C49)
unambiguous semidirect product(D3×C11×C49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C49
HallC3×C49×C11⋊C5 ⋊ C2
HallD3×C11×C49 ⋊ C5
HallC11×C49 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ C2×C49
HallC3×C49 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ C5×C49
SylowC11 ⋊ C5×D3×C49
SylowC3 ⋊ C2×C49×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC49D3×C11⋊C5
commutator, hypocenterC3×C11C2×C5×C49
FrattiniC7D3×C7×C11⋊C5
FittingC3×C11×C49C2×C5
socle, cosocleC3×C7×C11C2×C5×C7
prime radicalD3×C7×C11⋊C5C7
LCSG ▷ C3×C11
UCSC1 ◁ C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C49×AGL(1,𝔽11), D3×C49⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal normal subgroup ofD3×C49×AGL(1,𝔽11), D3×C49⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal quotient ofDic3×C49×C11⋊C5, C2×D3×C49×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 23);