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C5×C11⋊(D49⋊C3) #30633484

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(C5×D11)
unambiguous semidirect product(C5×D539)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C2×C3
derived, HallC11×C49 ⋊ C2×C3×C5
HallC5×C11×C49⋊C3 ⋊ C2
HallC5×D539 ⋊ C3
HallC11×C49⋊C3 ⋊ C2×C5
HallD539 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ D11
HallC5×C49 ⋊ C3×D11
HallC49⋊C3 ⋊ C5×D11
HallC5×C11 ⋊ D49⋊C3
SylowC49 ⋊ C3×C5×D11
SylowC11 ⋊ C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊(D49⋊C3)
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C5×C11⋊AGL(1,𝔽7)
FittingC5×C11×C49C2×C3
socleC5×C7×C11AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

545 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, 29);