Finite Group Databasebeta

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D3×C41×D13⋊C3 #34062935

order19188
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productD3×C41×D13⋊C3
unambiguous semidirect productD13⋊(C3×D3×C41)
unambiguous semidirect product(D3×D13)⋊(C3×C41)
unambiguous semidirect product(C3×D13⋊C3)⋊(C2×C41)
unambiguous semidirect product(D3×C13⋊C3)⋊(C2×C41)
unambiguous semidirect product(C3⋊(D13⋊C3))⋊(C2×C41)
unambiguous semidirect product(D3×D13×C41)⋊C3

Splittings

Fitting, socleC3×C13×C41 ⋊ C22×C3
derivedC3×C13 ⋊ C22×C3×C41
HallC3×C13⋊C3×C41 ⋊ C22
HallC13×C41 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C22×C41
SylowC13 ⋊ C2×C3×D3×C41

Subgroups

subgroupG/H
center, hypercenterC41D3×D13⋊C3
commutator, cosocle, hypocenterC3×C13C22×C3×C41
FrattiniC1G
Fitting, socleC3×C13×C41C22×C3
LCSG ▷ C3×C13
UCSC1 ◁ C41

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 87);