Finite Group Databasebeta

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C2×C9×D5×C11 #14520407

order1980
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D5×C11
unambiguous semidirect productC5⋊(C22×C9×C11)
unambiguous semidirect product(C2×C5)⋊(C2×C9×C11)

Splittings

FittingC2×C5×C9×C11 ⋊ C2
derived, SylowC5 ⋊ C22×C9×C11
HallC5×C9×C11 ⋊ C22
HallC5×C11 ⋊ C22×C9
HallC5×C9 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D5
commutator, hypocenterC5C22×C9×C11
FrattiniC3C2×C3×D5×C11
FittingC2×C5×C9×C11C2
socleC2×C3×C5×C11C2×C3
prime radicalC2×C3×D5×C11C3
cosocleC3×C5C22×C3×C11
LCSG ▷ C5
UCSC1 ◁ C2×C9×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 990

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C11×D7⋊C9, C2×C11×C5⋊(D7⋊C9), C2×D5×C11×C7⋊C9, …
maximal normal subgroup ofC2×C7×C9×D5×C11, C2×C9×D5×C121, C2×C9×D5×C112, …
maximal quotient ofD5×C11×D7⋊C9, C2×C11×C5⋊(D7⋊C9), C2×D5×C11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 32);