Finite Group Databasebeta

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C3×C11⋊C5×C67⋊C3 #45684243

order33165
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊C5×C67⋊C3
unambiguous semidirect productC11⋊(C3×C5×C67⋊C3)
unambiguous semidirect product(C3×C11)⋊(C5×C67⋊C3)
unambiguous semidirect productC67⋊(C32×C11⋊C5)
unambiguous semidirect product(C3×C67)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C67⋊C3)⋊(C3×C5)
unambiguous semidirect product(C11⋊C5×C67)⋊C32
unambiguous semidirect product(C3×C11×C67⋊C3)⋊C5
unambiguous semidirect product(C3×C11⋊C5×C67)⋊C3

Splittings

Fitting, socleC3×C11×C67 ⋊ C3×C5
derived, HallC11×C67 ⋊ C32×C5
HallC3×C11×C67⋊C3 ⋊ C5
HallC11⋊C5×C67 ⋊ C32
SylowC67 ⋊ C32×C11⋊C5
SylowC11 ⋊ C3×C5×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C67⋊C3
commutator, cosocle, hypocenterC11×C67C32×C5
FrattiniC1G
Fitting, socleC3×C11×C67C3×C5
LCSG ▷ C11×C67
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2211

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33165, 9);