Finite Group Databasebeta

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C2×C3×C47×D19⋊C3 #44565314

order32148
automorphism?
homologyAbelianization (H1) = C22×C32×C47 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C47×D19⋊C3
unambiguous semidirect productD19⋊(C2×C32×C47)
unambiguous semidirect product(C19⋊C3)⋊(C22×C3×C47)
unambiguous semidirect product(C2×D19)⋊(C32×C47)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C3×C47)
unambiguous semidirect product(C2×C3×D19)⋊(C3×C47)
unambiguous semidirect product(C2×D19×C47)⋊C32
unambiguous semidirect product(C2×C3×D19×C47)⋊C3

Splittings

Fitting, socleC2×C3×C19×C47 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C32×C47
HallC3×C47×C19⋊C3 ⋊ C22
HallC2×D19×C47 ⋊ C32
HallC19×C47 ⋊ C22×C32
HallC3×C19⋊C3 ⋊ C22×C47
HallC2×D19 ⋊ C32×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C47D19⋊C3
commutator, cosocle, hypocenterC19C22×C32×C47
FrattiniC1G
Fitting, socleC2×C3×C19×C47C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C47

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5358

Conjugacy classes & character table

2538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 74);