Finite Group Databasebeta

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C3×C5×C13×AGL(1,𝔽13) #44477908

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C13×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C32×C5×C13)
unambiguous semidirect product(C3×#261)⋊(C3×C5×C13)
unambiguous semidirect product(C5×#261)⋊(C32×C13)
unambiguous semidirect product(C3×C5×#261)⋊(C3×C13)

Splittings

Fitting, socleC3×C5×C132 ⋊ C3×C4
derivedC13 ⋊ C32×C4×C5×C13
HallC3×C5×C13×C13⋊C3 ⋊ C4
HallC5×C13×#261 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ C4×C5
HallC5×C132 ⋊ C32×C4
HallC13×#261 ⋊ C32×C5
SylowC132 ⋊ C32×C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13AGL(1,𝔽13)
commutator, hypocenterC13C32×C4×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C5×C13×D13⋊C3C2
cosocleD13C2×C32×C5×C13
LCSG ▷ C13
UCSC1 ◁ C3×C5×C13

148 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 2340

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 497);