Finite Group Databasebeta

← Prev (#43274885) Next (#43274887) →

C2×C3×C11×D73⋊C3 #43274886

order28908
automorphism?
homologyAbelianization (H1) = C22×C32×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C11×D73⋊C3
unambiguous semidirect productD73⋊(C2×C32×C11)
unambiguous semidirect product(C73⋊C3)⋊(C22×C3×C11)
unambiguous semidirect product(C2×D73)⋊(C32×C11)
unambiguous semidirect product(C2×C73⋊C3)⋊(C2×C3×C11)
unambiguous semidirect product(C2×C3×D73)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D73)⋊C32
unambiguous semidirect product(C2×C3×C11×D73)⋊C3

Splittings

Fitting, socleC2×C3×C11×C73 ⋊ C2×C3
derived, SylowC73 ⋊ C22×C32×C11
HallC3×C11×C73⋊C3 ⋊ C22
HallC2×C11×D73 ⋊ C32
HallC11×C73 ⋊ C22×C32
HallC3×C73⋊C3 ⋊ C22×C11
HallC2×D73 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D73⋊C3
commutator, cosocle, hypocenterC73C22×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C73C2×C3
LCSG ▷ C73
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4818

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28908, 86);