Finite Group Databasebeta

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C2×C9×C19×C11⋊C5 #34037809

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C19 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC2×C9×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C2×C5×C9×C19
HallC9×C11×C19 ⋊ C2×C5
HallC2×C11×C19 ⋊ C5×C9
HallC11×C19 ⋊ C2×C5×C9
HallC2×C9×C11 ⋊ C5×C19
HallC9×C11 ⋊ C2×C5×C19
HallC2×C11 ⋊ C5×C9×C19

Subgroups

subgroupG/H
center, hypercenterC2×C9×C19C11⋊C5
commutator, hypocenterC11C2×C5×C9×C19
FrattiniC3C2×C3×C19×C11⋊C5
FittingC2×C9×C11×C19C5
socleC2×C3×C11×C19C3×C5
prime radicalC2×C3×C19×C11⋊C5C3
cosocleC3×C11C2×C3×C5×C19
LCSG ▷ C11
UCSC1 ◁ C2×C9×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C9×C19×C11⋊C5, C9×C11⋊C5×Dic19, C9×C19×Dic11⋊C5, …
maximal normal subgroup ofC4×C9×C19×C11⋊C5, C9×C11⋊C5×Dic19, C9×C19×Dic11⋊C5, …
maximal quotient ofC4×C9×C19×C11⋊C5, C22×C9×C19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 2);