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C11×C5⋊(D49⋊C3) #30633487

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(D49⋊C3)
unambiguous semidirect productC5⋊(C11×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(D5×C11)
unambiguous semidirect productD245⋊(C3×C11)
unambiguous semidirect product(C11×D245)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C11
HallC5×C11×C49⋊C3 ⋊ C2
HallC11×D245 ⋊ C3
HallC11×C49⋊C3 ⋊ D5
HallC5×C49⋊C3 ⋊ C2×C11
HallC11×C49 ⋊ C3×D5
HallD245 ⋊ C3×C11
HallC49⋊C3 ⋊ D5×C11
HallC5×C11 ⋊ D49⋊C3
SylowC49 ⋊ C3×D5×C11
SylowC5 ⋊ C11×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(D49⋊C3)
commutator, cosocle, hypocenterC5×C49C2×C3×C11
FrattiniC7C11×C5⋊AGL(1,𝔽7)
FittingC5×C11×C49C2×C3
socleC5×C7×C11AGL(1,𝔽7)
LCSG ▷ C5×C49
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD11×C5⋊(D49⋊C3), D5×C11×D49⋊C3, D55⋊(D49⋊C3), …
maximal normal subgroup ofD11×C5⋊(D49⋊C3), D5×C11×D49⋊C3, D55⋊(D49⋊C3), …
maximal quotient ofC11×(C49⋊C3)⋊Dic5, C2×C11×C5⋊(D49⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 32);