Finite Group Databasebeta

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C3×C4×C13⋊C3×C47 #36347208

order21996
automorphism?
homologyAbelianization (H1) = C32×C4×C47 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13⋊C3×C47
unambiguous semidirect product(C4×C13)⋊(C32×C47)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C47)
unambiguous semidirect product(C4×C13×C47)⋊C32
unambiguous semidirect product(C3×C4×C13×C47)⋊C3

Splittings

FittingC3×C4×C13×C47 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C47
HallC4×C13×C47 ⋊ C32
HallC13×C47 ⋊ C32×C4
HallC4×C13 ⋊ C32×C47

Subgroups

subgroupG/H
center, hypercenterC3×C4×C47C13⋊C3
commutator, hypocenterC13C32×C4×C47
FrattiniC2C2×C3×C13⋊C3×C47
FittingC3×C4×C13×C47C3
socleC2×C3×C13×C47C2×C3
prime radicalC2×C3×C13⋊C3×C47C2
cosocleC2×C13C2×C32×C47
LCSG ▷ C13
UCSC1 ◁ C3×C4×C47

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7332

Conjugacy classes & character table

3948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 49);