Finite Group Databasebeta

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C3×C4×C13⋊C3×C41 #34062909

order19188
automorphism?
homologyAbelianization (H1) = C32×C4×C41 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13⋊C3×C41
unambiguous semidirect product(C4×C13)⋊(C32×C41)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C41)
unambiguous semidirect product(C4×C13×C41)⋊C32
unambiguous semidirect product(C3×C4×C13×C41)⋊C3

Splittings

FittingC3×C4×C13×C41 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C41
HallC4×C13×C41 ⋊ C32
HallC13×C41 ⋊ C32×C4
HallC4×C13 ⋊ C32×C41

Subgroups

subgroupG/H
center, hypercenterC3×C4×C41C13⋊C3
commutator, hypocenterC13C32×C4×C41
FrattiniC2C2×C3×C13⋊C3×C41
FittingC3×C4×C13×C41C3
socleC2×C3×C13×C41C2×C3
prime radicalC2×C3×C13⋊C3×C41C2
cosocleC2×C13C2×C32×C41
LCSG ▷ C13
UCSC1 ◁ C3×C4×C41

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

3444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 61);