Finite Group Databasebeta

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C3×C5×C19×C11⋊C5 #30627870

order15675
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C52×C19 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C19×C11⋊C5
unambiguous semidirect productC11⋊(C3×C52×C19)
unambiguous semidirect product(C3×C11)⋊(C52×C19)
unambiguous semidirect product(C5×C11)⋊(C3×C5×C19)
unambiguous semidirect product(C3×C5×C11)⋊(C5×C19)
unambiguous semidirect product(C3×C11×C19)⋊C52
unambiguous semidirect product(C3×C5×C11×C19)⋊C5

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C3×C52×C19
HallC3×C11×C19 ⋊ C52
HallC11×C19 ⋊ C3×C52
HallC3×C11 ⋊ C52×C19

Subgroups

subgroupG/H
center, hypercenterC3×C5×C19C11⋊C5
commutator, cosocle, hypocenterC11C3×C52×C19
FrattiniC1G
Fitting, socleC3×C5×C11×C19C5
LCSG ▷ C11
UCSC1 ◁ C3×C5×C19

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C19×AGL(1,𝔽11), C3×C5×C19⋊AGL(1,𝔽11), C3×C5×D19×C11⋊C5, …
maximal normal subgroup ofC3×C5×C19×AGL(1,𝔽11), C3×C5×C19⋊AGL(1,𝔽11), C3×C5×D19×C11⋊C5, …
maximal quotient ofC2×C3×C5×C19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15675, 7);