Finite Group Databasebeta

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C5×C7×C3⋊AGL(1,𝔽13) #30655386

order16380
isoclinismisoclinic class of C3⋊AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C3⋊AGL(1,𝔽13)
unambiguous semidirect productC3⋊(C5×C7×AGL(1,𝔽13))
unambiguous semidirect product(C3⋊#261)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C3⋊#261)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derivedC3×C13 ⋊ C3×C4×C5×C7
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC3×C7×C13⋊C3 ⋊ C4×C5
HallC3×C5×C13⋊C3 ⋊ C4×C7
HallC5×C7×C13 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C5×C7
HallC7×C13 ⋊ C3×C5×Dic3
HallC5×C13 ⋊ C3×C7×Dic3
SylowC13 ⋊ C3×C5×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊AGL(1,𝔽13)
commutator, hypocenterC3×C13C3×C4×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×C7×D13⋊C3C2
cosocleC3×D13C2×C3×C5×C7
LCSG ▷ C3×C13
UCSC1 ◁ C5×C7

112 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 436);