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C3×C11⋊C5×D49 #30633476

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

Aliases

direct productC3×C11⋊C5×D49
unambiguous semidirect product(C3×C11×D49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C2×C5
derived, HallC11×C49 ⋊ C2×C3×C5
HallC3×C49×C11⋊C5 ⋊ C2
HallC3×C11×D49 ⋊ C5
HallC49×C11⋊C5 ⋊ C2×C3
HallC11×D49 ⋊ C3×C5
HallC3×C49 ⋊ C2×C11⋊C5
SylowC49 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×D49
SylowC11 ⋊ C3×C5×D49

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D49
commutator, cosocle, hypocenterC11×C49C2×C3×C5
FrattiniC7C3×D7×C11⋊C5
FittingC3×C11×C49C2×C5
socleC3×C7×C11C5×D7
LCSG ▷ C11×C49
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D49×AGL(1,𝔽11), D49×C3⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal normal subgroup ofC3×D49×AGL(1,𝔽11), D49×C3⋊AGL(1,𝔽11), D3×C11⋊C5×D49, …
maximal quotient ofC3×C11⋊C5×Dic49, C2×C3×C11⋊C5×D49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 21);