Finite Group Databasebeta

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C3×C49×C22⋊(C13⋊C3) #37524306

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

Aliases

direct productC3×C49×C22⋊(C13⋊C3)
unambiguous semidirect product(C22×C3)⋊(C13⋊C3×C49)
unambiguous semidirect product(C3×C13)⋊(A4×C49)

Splittings

FittingC22×C3×C13×C49 ⋊ C3
derived, HallC22×C13 ⋊ C32×C49
HallC22×C13×C49 ⋊ C32
HallC13×C49 ⋊ C3×A4
HallC22×C49 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×A4×C49
SylowC22 ⋊ C3×C13⋊C3×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C32×C49
FrattiniC7C3×C7×C22⋊(C13⋊C3)
FittingC22×C3×C13×C49C3
socleC22×C3×C7×C13C3×C7
prime radicalC3×C7×C22⋊(C13⋊C3)C7
cosocleC22×C7×C13C32×C7
LCSG ▷ C22×C13
UCSC1 ◁ C3×C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 251);