Finite Group Databasebeta

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C3×C11×A4×C71 #43244707

order28116
automorphism?
homologyAbelianization (H1) = C32×C11×C71 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C11×A4×C71
unambiguous semidirect productC22⋊(C32×C11×C71)
unambiguous semidirect product(C22×C3)⋊(C3×C11×C71)
unambiguous semidirect product(C22×C11)⋊(C32×C71)
unambiguous semidirect product(C22×C3×C11)⋊(C3×C71)
unambiguous semidirect product(C22×C71)⋊(C32×C11)
unambiguous semidirect product(C22×C3×C71)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C71)⋊C32
unambiguous semidirect product(C22×C3×C11×C71)⋊C3

Splittings

Fitting, socleC22×C3×C11×C71 ⋊ C3
derived, SylowC22 ⋊ C32×C11×C71
HallC22×C11×C71 ⋊ C32
HallC22×C71 ⋊ C32×C11
HallC22×C11 ⋊ C32×C71

Subgroups

subgroupG/H
center, hypercenterC3×C11×C71A4
commutator, cosocle, hypocenterC22C32×C11×C71
FrattiniC1G
Fitting, socleC22×C3×C11×C71C3
LCSG ▷ C22
UCSC1 ◁ C3×C11×C71

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9372

Conjugacy classes & character table

9372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28116, 65);