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D3×C47×D13⋊C3 #36347227

order21996
automorphism?
homologyAbelianization (H1) = C22×C3×C47 · Schur multiplier (H2) = C2

Aliases

direct productD3×C47×D13⋊C3
unambiguous semidirect productD13⋊(C3×D3×C47)
unambiguous semidirect product(D3×D13)⋊(C3×C47)
unambiguous semidirect product(C3×D13⋊C3)⋊(C2×C47)
unambiguous semidirect product(D3×C13⋊C3)⋊(C2×C47)
unambiguous semidirect product(C3⋊(D13⋊C3))⋊(C2×C47)
unambiguous semidirect product(D3×D13×C47)⋊C3

Splittings

Fitting, socleC3×C13×C47 ⋊ C22×C3
derivedC3×C13 ⋊ C22×C3×C47
HallC3×C13⋊C3×C47 ⋊ C22
HallC13×C47 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C22×C47
SylowC13 ⋊ C2×C3×D3×C47

Subgroups

subgroupG/H
center, hypercenterC47D3×D13⋊C3
commutator, cosocle, hypocenterC3×C13C22×C3×C47
FrattiniC1G
Fitting, socleC3×C13×C47C22×C3
LCSG ▷ C3×C13
UCSC1 ◁ C47

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1833

Conjugacy classes & character table

1128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21996, 68);