Finite Group Databasebeta

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C5×C11×C3⋊D3×C19 #34037900

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C19 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C3⋊D3×C19
unambiguous semidirect productC3⋊(C5×D3×C11×C19)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C2
derived, SylowC32 ⋊ C2×C5×C11×C19
HallC32×C11×C19 ⋊ C2×C5
HallC32×C5×C19 ⋊ C2×C11
HallC32×C5×C11 ⋊ C2×C19
HallC32×C19 ⋊ C2×C5×C11
HallC32×C11 ⋊ C2×C5×C19
HallC32×C5 ⋊ C2×C11×C19

Subgroups

subgroupG/H
center, hypercenterC5×C11×C19C3⋊D3
commutator, cosocle, hypocenterC32C2×C5×C11×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C2
LCSG ▷ C32
UCSC1 ◁ C5×C11×C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

6270 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×C19×#157, C5×C11×C19⋊#157, C5×C19×C11⋊#157, …
maximal normal subgroup ofC5×C11×C19×#157, C5×C11×C19⋊#157, C5×C19×C11⋊#157, …
maximal quotient ofC5×C11×C19×C3⋊Dic3, C2×C5×C11×C3⋊D3×C19

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 93);