Finite Group Databasebeta

← Prev (#28410870) Next (#28410872) →

C2×C3×C11×D37⋊C3 #28410871

order14652
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×D37⋊C3
unambiguous semidirect productD37⋊(C2×C32×C11)
unambiguous semidirect product(C37⋊C3)⋊(C22×C3×C11)
unambiguous semidirect product(C2×D37)⋊(C32×C11)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×C3×D37)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D37)⋊C32
unambiguous semidirect product(C2×C3×C11×D37)⋊C3

Splittings

Fitting, socleC2×C3×C11×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C22×C32×C11
HallC3×C11×C37⋊C3 ⋊ C22
HallC2×C11×D37 ⋊ C32
HallC11×C37 ⋊ C22×C32
HallC3×C37⋊C3 ⋊ C22×C11
HallC2×D37 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D37⋊C3
commutator, cosocle, hypocenterC37C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 86);