Finite Group Databasebeta

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A4×C13⋊C3×C49 #37524232

order22932
automorphism?
homologyAbelianization (H1) = C32×C49 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×C13⋊C3×C49
unambiguous semidirect product(C22×C13⋊C3)⋊(C3×C49)
unambiguous semidirect product(A4×C13)⋊(C3×C49)
unambiguous semidirect product(C22⋊(C13⋊C3))⋊(C3×C49)

Splittings

Fitting, HallC22×C13×C49 ⋊ C32
derived, HallC22×C13 ⋊ C32×C49
HallC13×C49 ⋊ C3×A4
HallC22×C49 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×A4×C49
SylowC22 ⋊ C3×C13⋊C3×C49

Subgroups

subgroupG/H
center, hypercenterC49A4×C13⋊C3
commutator, hypocenterC22×C13C32×C49
FrattiniC7C7×A4×C13⋊C3
FittingC22×C13×C49C32
socle, cosocleC22×C7×C13C32×C7
prime radicalC7×A4×C13⋊C3C7
LCSG ▷ C22×C13
UCSC1 ◁ C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2548

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 177);