Finite Group Databasebeta

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C4×C11⋊C5×C43⋊C3 #43248757

order28380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11⋊C5×C43⋊C3
unambiguous semidirect product(C4×C11)⋊(C5×C43⋊C3)
unambiguous semidirect product(C4×C43)⋊(C3×C11⋊C5)
unambiguous semidirect product(C4×C11×C43⋊C3)⋊C5
unambiguous semidirect product(C4×C43×C11⋊C5)⋊C3

Splittings

Fitting, HallC4×C11×C43 ⋊ C3×C5
derived, HallC11×C43 ⋊ C3×C4×C5
HallC4×C43×C11⋊C5 ⋊ C3
HallC4×C11×C43⋊C3 ⋊ C5
HallC43×C11⋊C5 ⋊ C3×C4
HallC11×C43⋊C3 ⋊ C4×C5
HallC4×C43 ⋊ C3×C11⋊C5
HallC4×C11 ⋊ C5×C43⋊C3
SylowC43 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C4×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C11⋊C5×C43⋊C3
commutator, hypocenterC11×C43C3×C4×C5
FrattiniC2C2×C11⋊C5×C43⋊C3
FittingC4×C11×C43C3×C5
socle, cosocleC2×C11×C43C2×C3×C5
prime radicalC2×C11⋊C5×C43⋊C3C2
LCSG ▷ C11×C43
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1892

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 4);