Finite Group Databasebeta

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C3×C4×C5×C11×C19⋊C3 #49178478

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C11 · Schur multiplier (H2) = C3

Aliases

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

Splittings

FittingC3×C4×C5×C11×C19 ⋊ C3
derived, SylowC19 ⋊ C32×C4×C5×C11
HallC4×C5×C11×C19 ⋊ C32
HallC5×C11×C19 ⋊ C32×C4
HallC4×C11×C19 ⋊ C32×C5
HallC4×C5×C19 ⋊ C32×C11
HallC11×C19 ⋊ C32×C4×C5
HallC5×C19 ⋊ C32×C4×C11
HallC4×C19 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C11C19⋊C3
commutator, hypocenterC19C32×C4×C5×C11
FrattiniC2C2×C3×C5×C11×C19⋊C3
FittingC3×C4×C5×C11×C19C3
socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C11×C19⋊C3C2
cosocleC2×C19C2×C32×C5×C11
LCSG ▷ C19
UCSC1 ◁ C3×C4×C5×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12540

Conjugacy classes & character table

5940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 187);