Finite Group Databasebeta

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C3×C13×#63122⋊C3 #44477929

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

Aliases

direct productC3×C13×#63122⋊C3
unambiguous semidirect product#63122⋊(C32×C13)
unambiguous semidirect product(C3×#63122)⋊(C3×C13)

Splittings

Fitting, socleC3×C5×C132 ⋊ C3×C4
derivedC5×C13 ⋊ C32×C4×C13
HallC3×C5×C13×C13⋊C3 ⋊ C4
HallC13×#63122 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C132 ⋊ C32×C4
SylowC132 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×C13×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3×C13#63122⋊C3
commutator, hypocenterC5×C13C32×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×C13×C5⋊(D13⋊C3)C2
cosocleD65C2×C32×C13
LCSG ▷ C5×C13
UCSC1 ◁ C3×C13

148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 518);