Finite Group Databasebeta

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C3×C4×C13⋊C3×C49 #37524165

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C49 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C13⋊C3×C49
unambiguous semidirect product(C4×C13)⋊(C32×C49)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C49)

Splittings

FittingC3×C4×C13×C49 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C49
HallC4×C13×C49 ⋊ C32
HallC13×C49 ⋊ C32×C4
HallC4×C13 ⋊ C32×C49

Subgroups

subgroupG/H
center, hypercenterC3×C4×C49C13⋊C3
commutator, hypocenterC13C32×C4×C49
FrattiniC2×C7C2×C3×C7×C13⋊C3
FittingC3×C4×C13×C49C3
socleC2×C3×C7×C13C2×C3×C7
prime radicalC2×C3×C7×C13⋊C3C2×C7
cosocleC2×C7×C13C2×C32×C7
LCSG ▷ C13
UCSC1 ◁ C3×C4×C49

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 110);