Finite Group Databasebeta

← Prev (#49178448) Next (#49178450) →

C3×C4×C11⋊C5×C19⋊C3 #49178449

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C11⋊C5×C19⋊C3
unambiguous semidirect product(C4×C11)⋊(C3×C5×C19⋊C3)
unambiguous semidirect product(C4×C19)⋊(C32×C11⋊C5)
unambiguous semidirect product(C3×C4×C11)⋊(C5×C19⋊C3)
unambiguous semidirect product(C3×C4×C19)⋊(C3×C11⋊C5)
unambiguous semidirect product(C4×C11×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×C19×C11⋊C5)⋊C32
unambiguous semidirect product(C3×C4×C11×C19⋊C3)⋊C5
unambiguous semidirect product(C3×C4×C19×C11⋊C5)⋊C3

Splittings

FittingC3×C4×C11×C19 ⋊ C3×C5
derived, HallC11×C19 ⋊ C32×C4×C5
HallC3×C4×C11×C19⋊C3 ⋊ C5
HallC4×C19×C11⋊C5 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C32×C4
HallC4×C11×C19 ⋊ C32×C5
HallC4×C19 ⋊ C32×C11⋊C5
HallC4×C11 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C32×C4×C11⋊C5
SylowC11 ⋊ C3×C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C4C11⋊C5×C19⋊C3
commutator, hypocenterC11×C19C32×C4×C5
FrattiniC2C2×C3×C11⋊C5×C19⋊C3
FittingC3×C4×C11×C19C3×C5
socleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×C11⋊C5×C19⋊C3C2
cosocleC2×C11×C19C2×C32×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3×C4

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 158);