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C3×C13×C3⋊(C7⋊AGL(1,𝔽5)) #30655646

order16380
isoclinismisoclinic class of C3⋊(C7⋊AGL(1,𝔽5))
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C3⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C3×C13×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derivedC3×C5×C7 ⋊ C3×C4×C13
HallC32×C7×C13 ⋊ AGL(1,𝔽5)
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ C3×Dic3
HallC32×C5×C7 ⋊ C4×C13
HallC32×C13 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C13 ⋊ C3×ΓL(1,𝔽16)
HallC5×C13 ⋊ C3×Dic21
HallC32×C7 ⋊ C13×AGL(1,𝔽5)
HallC32×C5 ⋊ C13×Dic7
HallC5×C7 ⋊ C3×Dic3×C13
SylowC32 ⋊ C13×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C3×C13×ΓL(1,𝔽16)
SylowC5 ⋊ C3×C13×Dic21

Subgroups

subgroupG/H
center, hypercenterC3×C13C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C3×C4×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC32×C7×D5×C13C2
cosocleC3×C7×D5C2×C3×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C13

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 2730

Conjugacy classes & character table

1755 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 696);