Finite Group Databasebeta

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C3×C5×C7×AGL(1,𝔽13) #30655310

order16380
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C32×C5×C7)
unambiguous semidirect product(C3×#261)⋊(C3×C5×C7)
unambiguous semidirect product(C5×#261)⋊(C32×C7)
unambiguous semidirect product(C3×C5×#261)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, SylowC13 ⋊ C32×C4×C5×C7
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC5×C7×#261 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ C4×C5
HallC3×C5×C13⋊C3 ⋊ C4×C7
HallC5×C7×C13 ⋊ C32×C4
HallC7×#261 ⋊ C32×C5
HallC5×#261 ⋊ C32×C7
HallC3×C13⋊C3 ⋊ C4×C5×C7
HallC7×C13 ⋊ C32×C4×C5
HallC5×C13 ⋊ C32×C4×C7
Hall#261 ⋊ C32×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7AGL(1,𝔽13)
commutator, hypocenterC13C32×C4×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13⋊C3C2
cosocleD13C2×C32×C5×C7
LCSG ▷ C13
UCSC1 ◁ C3×C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 360);