Finite Group Databasebeta

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C13×C3⋊(#63118⋊C3) #44478070

order30420
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(#63118⋊C3)
unambiguous semidirect productC3⋊(C13×#63118⋊C3)
unambiguous semidirect product(C3⋊#63118)⋊(C3×C13)

Splittings

Fitting, socleC3×C5×C132 ⋊ C3×C4
derivedC3×C5×C13 ⋊ C3×C4×C13
HallC3×C5×C13×C13⋊C3 ⋊ C4
HallC3×C13×C13⋊C3 ⋊ Dic5
HallC5×C132 ⋊ C3×Dic3
SylowC132 ⋊ C3×Dic15
SylowC5 ⋊ C13×C3⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(#63118⋊C3)
commutator, hypocenterC3×C5×C13C3×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C5×C13×D13⋊C3C2
cosocleC3×C5×D13C2×C3×C13
LCSG ▷ C3×C5×C13
UCSC1 ◁ C13

116 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 44 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 659);