Finite Group Databasebeta

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C3×C4×C47×C19⋊C3 #44565287

order32148
automorphism?
homologyAbelianization (H1) = C32×C4×C47 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C47×C19⋊C3
unambiguous semidirect product(C4×C19)⋊(C32×C47)
unambiguous semidirect product(C3×C4×C19)⋊(C3×C47)
unambiguous semidirect product(C4×C19×C47)⋊C32
unambiguous semidirect product(C3×C4×C19×C47)⋊C3

Splittings

FittingC3×C4×C19×C47 ⋊ C3
derived, SylowC19 ⋊ C32×C4×C47
HallC4×C19×C47 ⋊ C32
HallC19×C47 ⋊ C32×C4
HallC4×C19 ⋊ C32×C47

Subgroups

subgroupG/H
center, hypercenterC3×C4×C47C19⋊C3
commutator, hypocenterC19C32×C4×C47
FrattiniC2C2×C3×C47×C19⋊C3
FittingC3×C4×C19×C47C3
socleC2×C3×C19×C47C2×C3
prime radicalC2×C3×C47×C19⋊C3C2
cosocleC2×C19C2×C32×C47
LCSG ▷ C19
UCSC1 ◁ C3×C4×C47

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10716

Conjugacy classes & character table

5076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 47);