Finite Group Databasebeta

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C3×C13×#63120⋊C3 #44477928

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

Aliases

direct productC3×C13×#63120⋊C3
unambiguous semidirect product#63120⋊(C32×C13)
unambiguous semidirect product(C3×#63120)⋊(C3×C13)

Splittings

Fitting, socleC3×C5×C132 ⋊ C3×C4
derivedC5×C13 ⋊ C32×C4×C13
HallC3×C5×C13×C13⋊C3 ⋊ C4
HallC13×#63120 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C132 ⋊ C32×C4
SylowC132 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×C13×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C13#63120⋊C3
commutator, hypocenterC5×C13C32×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C132C3×C4
prime radicalC3×D5×C13×C13⋊C3C2
cosocleD5×C13C2×C32×C13
LCSG ▷ C5×C13
UCSC1 ◁ C3×C13

160 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1170

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, 517);