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C5×C11×D147 #30633469

order16170
isoclinismisoclinic class of D147
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D147
unambiguous semidirect productC3⋊(C5×C11×D49)
unambiguous semidirect productC49⋊(C5×D3×C11)

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C2
derived, HallC3×C49 ⋊ C2×C5×C11
HallC5×C11×C49 ⋊ D3
HallC3×C11×C49 ⋊ C2×C5
HallC3×C5×C49 ⋊ C2×C11
HallC11×C49 ⋊ C5×D3
HallC5×C49 ⋊ D3×C11
HallC3×C5×C11 ⋊ D49
SylowC49 ⋊ C5×D3×C11
HallC3×C11 ⋊ C5×D49
HallC3×C5 ⋊ C11×D49
SylowC3 ⋊ C5×C11×D49

Subgroups

subgroupG/H
center, hypercenterC5×C11D147
commutator, cosocle, hypocenterC3×C49C2×C5×C11
FrattiniC7C5×C11×D21
FittingC3×C5×C11×C49C2
socleC3×C5×C7×C11D7
LCSG ▷ C3×C49
UCSC1 ◁ C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4125 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×D147, C5×D3×C11×D49, C5×D33⋊D49, …
maximal normal subgroup ofC5×D11×D147, C5×D3×C11×D49, C5×D33⋊D49, …
maximal quotient ofC5×C11×Dic147, C2×C5×C11×D147

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 14);