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A4×C13⋊C3×C47 #36347232

order21996
automorphism?
homologyAbelianization (H1) = C32×C47 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×C13⋊C3×C47
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C47)
unambiguous semidirect product(A4×C13)⋊(C3×C47)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C47)
unambiguous semidirect product(C47×C22⋊(C13⋊C3))⋊C3
unambiguous semidirect product(A4×C13×C47)⋊C3
unambiguous semidirect product(C22×C13⋊C3×C47)⋊C3

Splittings

Fitting, socle, HallC22×C13×C47 ⋊ C32
derived, HallC22×C13 ⋊ C32×C47
HallC13×C47 ⋊ C3×A4
HallC22×C47 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×A4×C47
SylowC22 ⋊ C3×C13⋊C3×C47

Subgroups

subgroupG/H
center, hypercenterC47A4×C13⋊C3
commutator, cosocle, hypocenterC22×C13C32×C47
FrattiniC1G
Fitting, socleC22×C13×C47C32
LCSG ▷ C22×C13
UCSC1 ◁ C47

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2444

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 73);