Finite Group Databasebeta

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C3×C49×D37⋊C3 #45657262

order32634
automorphism?
homologyAbelianization (H1) = C2×C32×C49 · Schur multiplier (H2) = C3

Aliases

direct productC3×C49×D37⋊C3
unambiguous semidirect productD37⋊(C32×C49)
unambiguous semidirect product(C37⋊C3)⋊(C2×C3×C49)
unambiguous semidirect product(C3×D37)⋊(C3×C49)

Splittings

FittingC3×C37×C49 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C32×C49
HallC3×C49×C37⋊C3 ⋊ C2
HallC49×D37 ⋊ C32
HallC37×C49 ⋊ C2×C32
HallC3×C37⋊C3 ⋊ C2×C49
HallD37 ⋊ C32×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49D37⋊C3
commutator, hypocenterC37C2×C32×C49
FrattiniC7C3×C7×D37⋊C3
FittingC3×C37×C49C2×C3
socleC3×C7×C37C2×C3×C7
prime radicalC3×C7×D37⋊C3C7
cosocleC7×C37C2×C32×C7
LCSG ▷ C37
UCSC1 ◁ C3×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5439

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32634, 42);