Finite Group Databasebeta

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C3×C4×C43×C19⋊C3 #44440950

order29412
automorphism?
homologyAbelianization (H1) = C32×C4×C43 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C43×C19⋊C3
unambiguous semidirect product(C4×C19)⋊(C32×C43)
unambiguous semidirect product(C3×C4×C19)⋊(C3×C43)

Splittings

FittingC3×C4×C19×C43 ⋊ C3
derived, SylowC19 ⋊ C32×C4×C43
HallC4×C19×C43 ⋊ C32
HallC19×C43 ⋊ C32×C4
HallC4×C19 ⋊ C32×C43

Subgroups

subgroupG/H
center, hypercenterC3×C4×C43C19⋊C3
commutator, hypocenterC19C32×C4×C43
FrattiniC2C2×C3×C43×C19⋊C3
FittingC3×C4×C19×C43C3
socleC2×C3×C19×C43C2×C3
prime radicalC2×C3×C43×C19⋊C3C2
cosocleC2×C19C2×C32×C43
LCSG ▷ C19
UCSC1 ◁ C3×C4×C43

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9804

Conjugacy classes & character table

4644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29412, 112);