Finite Group Databasebeta

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C3⋊D3×D19×C11⋊C5 #49178561

order37620
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3⋊D3×D19×C11⋊C5
unambiguous semidirect product(C3×D19)⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×C3⋊D3×D19)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C19 ⋊ C22×C5
HallC32×C19×C11⋊C5 ⋊ C22
HallC11×C3⋊D3×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C3⋊D3
HallC32×C11⋊C5 ⋊ C2×D19
HallC11×C19 ⋊ C2×C5×C3⋊D3
HallC32×C19 ⋊ C22×C11⋊C5
HallC32×C11 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C3⋊D3×C11⋊C5
SylowC11 ⋊ C5×C3⋊D3×D19
SylowC32 ⋊ C2×D19×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C19C22×C5
LCSG ▷ C32×C11×C19
UCSC1

240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 1881

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 270);