Finite Group Databasebeta

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C2×D9×C19×C11⋊C5 #49178359

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×D9×C19×C11⋊C5
unambiguous semidirect productC9⋊(C22×C19×C11⋊C5)
unambiguous semidirect product(C2×C9)⋊(C2×C19×C11⋊C5)
unambiguous semidirect product(C2×C11×D9)⋊(C5×C19)
unambiguous semidirect product(C2×C11×D9×C19)⋊C5

Splittings

FittingC2×C9×C11×C19 ⋊ C2×C5
derived, HallC9×C11 ⋊ C22×C5×C19
HallC9×C19×C11⋊C5 ⋊ C22
HallC2×C11×D9×C19 ⋊ C5
HallC9×C11×C19 ⋊ C22×C5
HallC9×C11⋊C5 ⋊ C22×C19
HallC2×C11×D9 ⋊ C5×C19
HallC11×C19 ⋊ C2×C5×D9
HallC9×C19 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D9×C19
SylowC9 ⋊ C22×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C19D9×C11⋊C5
commutator, cosocle, hypocenterC9×C11C22×C5×C19
FrattiniC3C2×D3×C19×C11⋊C5
FittingC2×C9×C11×C19C2×C5
socleC2×C3×C11×C19C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C2×C19

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

1596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 68);