Finite Group Databasebeta

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C3×A4×C13×C49 #37524307

order22932
automorphism?
homologyAbelianization (H1) = C32×C13×C49 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C13×C49
unambiguous semidirect productC22⋊(C32×C13×C49)
unambiguous semidirect product(C22×C3)⋊(C3×C13×C49)

Splittings

FittingC22×C3×C13×C49 ⋊ C3
derived, SylowC22 ⋊ C32×C13×C49
HallC22×C13×C49 ⋊ C32
HallC22×C49 ⋊ C32×C13
HallC22×C13 ⋊ C32×C49

Subgroups

subgroupG/H
center, hypercenterC3×C13×C49A4
commutator, hypocenterC22C32×C13×C49
FrattiniC7C3×C7×A4×C13
FittingC22×C3×C13×C49C3
socleC22×C3×C7×C13C3×C7
prime radicalC3×C7×A4×C13C7
cosocleC22×C7C32×C7×C13
LCSG ▷ C22
UCSC1 ◁ C3×C13×C49

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7644

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 252);