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C5×C11×D49⋊C3 #30633483

order16170
isoclinismisoclinic class of D49⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D49⋊C3
unambiguous semidirect productD49⋊(C3×C5×C11)
unambiguous semidirect product(C49⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D49)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D49)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C2×C3×C5×C11
HallC5×C11×C49⋊C3 ⋊ C2
HallC5×C11×D49 ⋊ C3
HallC11×C49⋊C3 ⋊ C2×C5
HallC11×D49 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ C2×C11
HallC11×C49 ⋊ C2×C3×C5
HallC5×D49 ⋊ C3×C11
HallC5×C49 ⋊ C2×C3×C11
HallC49⋊C3 ⋊ C2×C5×C11
HallD49 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D49⋊C3
commutator, cosocle, hypocenterC49C2×C3×C5×C11
FrattiniC7C5×C11×AGL(1,𝔽7)
FittingC5×C11×C49C2×C3
socleC5×C7×C11AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×D49⋊C3, D5×C11×D49⋊C3, D55×D49⋊C3, …
maximal normal subgroup ofC5×D11×D49⋊C3, D5×C11×D49⋊C3, D55×D49⋊C3, …
maximal quotient ofC5×C11×(C49⋊C3)⋊C4, C2×C5×C11×D49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 28);