Finite Group Databasebeta

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C5×D3×C11×D19⋊C3 #49178583

order37620
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C11×D19⋊C3
unambiguous semidirect productD19⋊(C3×C5×D3×C11)
unambiguous semidirect product(D3×D19)⋊(C3×C5×C11)
unambiguous semidirect product(C3×D19⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(D3×C19⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C3⋊(D19⋊C3))⋊(C2×C5×C11)
unambiguous semidirect product(C5×D3×D19)⋊(C3×C11)
unambiguous semidirect product(C5×D3×C11×D19)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C11D3×D19⋊C3
commutator, cosocle, hypocenterC3×C19C22×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C22×C3
LCSG ▷ C3×C19
UCSC1 ◁ C5×C11

176 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 68 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

1485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 292);