Finite Group Databasebeta

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C3×D11×C5⋊(D19⋊C3) #49178579

order37620
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×D11×C5⋊(D19⋊C3)
unambiguous semidirect product(C5×D11)⋊(C3×D19⋊C3)
unambiguous semidirect product(D11×C19⋊C3)⋊(C3×D5)
unambiguous semidirect product(D11×D95)⋊C32
unambiguous semidirect product(C3×D11×D95)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C22×C3
derived, HallC5×C11×C19 ⋊ C22×C32
HallC3×C5×C11×C19⋊C3 ⋊ C22
HallD11×D95 ⋊ C32
HallC3×C11×C19⋊C3 ⋊ C2×D5
HallC3×C5×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C2×C32×D5
HallC3×C19⋊C3 ⋊ D5×D11
HallC5×C19 ⋊ C2×C32×D11
HallC5×C11 ⋊ C2×C3×D19⋊C3
SylowC19 ⋊ C32×D5×D11
SylowC11 ⋊ C2×C3×C5⋊(D19⋊C3)
SylowC5 ⋊ C3×D11×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D11×C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C11×C19C22×C32
FrattiniC1G
Fitting, socleC3×C5×C11×C19C22×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C3

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 288);