Finite Group Databasebeta

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C3×C4×C5×C7×C13⋊C3 #30655256

order16380
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C5×C7×C13⋊C3
unambiguous semidirect product(C4×C13)⋊(C32×C5×C7)
unambiguous semidirect product(C3×C4×C13)⋊(C3×C5×C7)
unambiguous semidirect product(C4×C5×C13)⋊(C32×C7)
unambiguous semidirect product(C3×C4×C5×C13)⋊(C3×C7)

Splittings

FittingC3×C4×C5×C7×C13 ⋊ C3
derived, SylowC13 ⋊ C32×C4×C5×C7
HallC4×C5×C7×C13 ⋊ C32
HallC5×C7×C13 ⋊ C32×C4
HallC4×C7×C13 ⋊ C32×C5
HallC4×C5×C13 ⋊ C32×C7
HallC7×C13 ⋊ C32×C4×C5
HallC5×C13 ⋊ C32×C4×C7
HallC4×C13 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C7C13⋊C3
commutator, hypocenterC13C32×C4×C5×C7
FrattiniC2C2×C3×C5×C7×C13⋊C3
FittingC3×C4×C5×C7×C13C3
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C7×C13⋊C3C2
cosocleC2×C13C2×C32×C5×C7
LCSG ▷ C13
UCSC1 ◁ C3×C4×C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

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(16380, 306);