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C2×D9×C11⋊C5 #14520391

order1980
isoclinismisoclinic class of D9×C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D9×C11⋊C5
unambiguous semidirect productC9⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×C9)⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×D9)⋊C5

Splittings

FittingC2×C9×C11 ⋊ C2×C5
derived, HallC9×C11 ⋊ C22×C5
HallC9×C11⋊C5 ⋊ C22
HallC2×C11×D9 ⋊ C5
SylowC11 ⋊ C2×C5×D9
SylowC9 ⋊ C22×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D9×C11⋊C5
commutator, cosocle, hypocenterC9×C11C22×C5
FrattiniC3C2×D3×C11⋊C5
FittingC2×C9×C11C2×C5
socleC2×C3×C11C5×D3
LCSG ▷ C9×C11
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 198

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D9×C11⋊C5, C2×C7×D9×C11⋊C5, C2×C11⋊C5×D63, …
maximal normal subgroup ofC2×C7×D9×C11⋊C5, C2×C11×D9×C11⋊C5, C2×C13×D9×C11⋊C5, …
maximal quotient ofD7×D9×C11⋊C5, C2×C7×D9×C11⋊C5, C2×C11⋊C5×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 16);