Finite Group Databasebeta

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C2×C3×C5×C11×C19⋊C3 #34037892

order18810
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C11×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C32×C5×C11)
unambiguous semidirect product(C2×C3×C19)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C19)⋊(C32×C11)
unambiguous semidirect product(C2×C3×C5×C19)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C19)⋊C32
unambiguous semidirect product(C2×C3×C5×C11×C19)⋊C3

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C3
derived, SylowC19 ⋊ C2×C32×C5×C11
HallC2×C5×C11×C19 ⋊ C32
HallC5×C11×C19 ⋊ C2×C32
HallC2×C11×C19 ⋊ C32×C5
HallC11×C19 ⋊ C2×C32×C5
HallC2×C5×C19 ⋊ C32×C11
HallC5×C19 ⋊ C2×C32×C11
HallC2×C19 ⋊ C32×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11C19⋊C3
commutator, cosocle, hypocenterC19C2×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

2970 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C11×(C19⋊C3)⋊C4, C3×C5×C11⋊((C19⋊C3)⋊C4), C3×C5×Dic11×C19⋊C3, …
maximal normal subgroup ofC3×C5×C11×(C19⋊C3)⋊C4, C3×C5×C11⋊((C19⋊C3)⋊C4), C3×C5×Dic11×C19⋊C3, …
maximal quotient ofC3×C4×C5×C11×C19⋊C3, C22×C3×C5×C11×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 85);