Finite Group Databasebeta

← Prev (#45657273) Next (#45657275) →

C49×C3⋊(D37⋊C3) #45657274

order32634
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C3⋊(D37⋊C3)
unambiguous semidirect productC3⋊(C49×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(D3×C49)
unambiguous semidirect productD111⋊(C3×C49)

Splittings

FittingC3×C37×C49 ⋊ C2×C3
derivedC3×C37 ⋊ C2×C3×C49
HallC3×C49×C37⋊C3 ⋊ C2
HallC37×C49 ⋊ C3×D3
HallC3×C37⋊C3 ⋊ C2×C49
SylowC37 ⋊ C3×D3×C49

Subgroups

subgroupG/H
center, hypercenterC49C3⋊(D37⋊C3)
commutator, hypocenterC3×C37C2×C3×C49
FrattiniC7C7×C3⋊(D37⋊C3)
FittingC3×C37×C49C2×C3
socle, cosocleC3×C7×C37C2×C3×C7
prime radicalC7×C3⋊(D37⋊C3)C7
LCSG ▷ C3×C37
UCSC1 ◁ C49

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5439

Conjugacy classes & character table

1323 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32634, 54);