Finite Group Databasebeta

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C3×C7×C11×C13⋊C3 #22583096

order9009
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C11×C13⋊C3
unambiguous semidirect productC13⋊(C32×C7×C11)
unambiguous semidirect product(C3×C13)⋊(C3×C7×C11)
unambiguous semidirect product(C11×C13)⋊(C32×C7)
unambiguous semidirect product(C3×C11×C13)⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C32×C7×C11
HallC7×C11×C13 ⋊ C32
HallC11×C13 ⋊ C32×C7
HallC7×C13 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11C13⋊C3
commutator, hypocenterC13C32×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C3×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×C11×D13⋊C3, C3×C7×C11⋊(D13⋊C3), C3×C7×D11×C13⋊C3, …
maximal normal subgroup ofC3×C7×C11×D13⋊C3, C3×C7×C11⋊(D13⋊C3), C3×C7×D11×C13⋊C3, …
maximal quotient ofC2×C3×C7×C11×C13⋊C3, C7×C11×A4×C13⋊C3, C3×C7×C11×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9009, 11);