Finite Group Databasebeta

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A4×C13⋊C3×C41 #34062941

order19188
automorphism?
homologyAbelianization (H1) = C32×C41 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×C13⋊C3×C41
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C41)
unambiguous semidirect product(A4×C13)⋊(C3×C41)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C41)
unambiguous semidirect product(C22×C13⋊C3×C41)⋊C3
unambiguous semidirect product(A4×C13×C41)⋊C3
unambiguous semidirect product(C41×C22⋊(C13⋊C3))⋊C3

Splittings

Fitting, socle, HallC22×C13×C41 ⋊ C32
derived, HallC22×C13 ⋊ C32×C41
HallC13×C41 ⋊ C3×A4
HallC22×C41 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×A4×C41
SylowC22 ⋊ C3×C13⋊C3×C41

Subgroups

subgroupG/H
center, hypercenterC41A4×C13⋊C3
commutator, cosocle, hypocenterC22×C13C32×C41
FrattiniC1G
Fitting, socleC22×C13×C41C32
LCSG ▷ C22×C13
UCSC1 ◁ C41

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 93);