Finite Group Databasebeta

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D3×D5×C11×C19⋊C3 #49178602

order37620
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×C11×C19⋊C3
unambiguous semidirect product(C5×D3)⋊(C2×C11×C19⋊C3)
unambiguous semidirect product(C3×D5)⋊(C2×C11×C19⋊C3)
unambiguous semidirect productD15⋊(C2×C11×C19⋊C3)
unambiguous semidirect product(D3×D5×C19)⋊(C3×C11)
unambiguous semidirect product(D3×D5×C11×C19)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C22×C3
derivedC3×C5×C19 ⋊ C22×C3×C11
HallC3×C5×C11×C19⋊C3 ⋊ C22
HallC3×C11×C19⋊C3 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3×D3
HallC3×C5×C19⋊C3 ⋊ C22×C11
HallC11×C19 ⋊ C3×D3×D5
HallC3×C19⋊C3 ⋊ C2×D5×C11
HallC5×C19 ⋊ C2×C3×D3×C11
HallC5×C11 ⋊ C2×D3×C19⋊C3
SylowC19 ⋊ C3×D3×D5×C11
SylowC5 ⋊ C2×D3×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D3×D5×C19⋊C3
commutator, cosocle, hypocenterC3×C5×C19C22×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C22×C3
LCSG ▷ C3×C5×C19
UCSC1 ◁ C11

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 311);