Finite Group Databasebeta

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C3×D5×C11×C19⋊C3 #34037880

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

Aliases

direct productC3×D5×C11×C19⋊C3
unambiguous semidirect productC5⋊(C2×C3×C11×C19⋊C3)
unambiguous semidirect product(D5×C19)⋊(C32×C11)
unambiguous semidirect product(C3×D5×C19)⋊(C3×C11)
unambiguous semidirect product(D5×C11×C19)⋊C32
unambiguous semidirect product(C3×D5×C11×C19)⋊C3

Splittings

Fitting, socleC3×C5×C11×C19 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C32×C11
HallC3×C5×C11×C19⋊C3 ⋊ C2
HallD5×C11×C19 ⋊ C32
HallC5×C11×C19 ⋊ C2×C32
HallC3×C5×C19⋊C3 ⋊ C2×C11
HallC11×C19 ⋊ C32×D5
HallD5×C19 ⋊ C32×C11
HallC5×C11 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C32×D5×C11
SylowC5 ⋊ C2×C3×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×C19⋊C3
commutator, cosocle, hypocenterC5×C19C2×C32×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C19C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C3×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×(C19⋊C3)⋊AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×C19⋊C3, C3×C11⋊((C19⋊C3)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC3×C11×(C19⋊C3)⋊AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×C19⋊C3, C3×C11⋊((C19⋊C3)⋊AGL(1,𝔽5)), …
maximal quotient ofC3×C11×Dic5×C19⋊C3, C2×C3×D5×C11×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 73);