Finite Group Databasebeta

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C2×C5×C9×D11 #14520406

order1980
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D11

Splittings

FittingC2×C5×C9×C11 ⋊ C2
derived, SylowC11 ⋊ C22×C5×C9
HallC5×C9×C11 ⋊ C22
HallC9×C11 ⋊ C22×C5
HallC5×C11 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D11
commutator, hypocenterC11C22×C5×C9
FrattiniC3C2×C3×C5×D11
FittingC2×C5×C9×C11C2
socleC2×C3×C5×C11C2×C3
prime radicalC2×C3×C5×D11C3
cosocleC3×C11C22×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 990

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×D7⋊C9, C2×C5×C11⋊(D7⋊C9), C2×C5×D11×C7⋊C9, …
maximal normal subgroup ofC2×C5×C7×C9×D11, C2×C5×C9×C11×D11, C2×C5×C9×C13×D11, …
maximal quotient ofC5×D11×D7⋊C9, C2×C5×C11⋊(D7⋊C9), C2×C5×D11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 31);