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C11⋊C5×D49⋊C3 #30633490

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

Aliases

direct productC11⋊C5×D49⋊C3
unambiguous semidirect productD49⋊(C3×C11⋊C5)
unambiguous semidirect product(C49⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D49⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×D49)⋊C3

Splittings

Fitting, derived, HallC11×C49 ⋊ C2×C3×C5
HallC11⋊C5×C49⋊C3 ⋊ C2
HallC11⋊C5×D49 ⋊ C3
HallC11×D49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallC11×C49⋊C3 ⋊ C2×C5
HallC11×D49 ⋊ C3×C5
HallC49⋊C3 ⋊ C2×C11⋊C5
HallD49 ⋊ C3×C11⋊C5
SylowC49 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7AGL(1,𝔽7)×C11⋊C5
socleC7×C11C5×AGL(1,𝔽7)
LCSG ▷ C11×C49
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 539

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽11)×D49⋊C3, C2×C11⋊C5×D49⋊C3
maximal normal subgroup ofAGL(1,𝔽11)×D49⋊C3, C2×C11⋊C5×D49⋊C3
maximal quotient ofC11⋊C5×(C49⋊C3)⋊C4, C2×C11⋊C5×D49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 35);