Finite Group Databasebeta

← Prev (#30655387) Next (#30655389) →

C5×C3⋊#11763985 #30655388

order16380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#11763985
unambiguous semidirect productC3⋊(C5×#11763985)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derivedC3×C7×C13 ⋊ C3×C4×C5
HallC3×C5×#63270 ⋊ C4
HallC3×#63270 ⋊ C4×C5
HallC5×C7×C13 ⋊ C3×Dic3
HallC7×C13 ⋊ C3×C5×Dic3
HallC5×C13 ⋊ C3⋊(ΓL(1,𝔽8)⋊C4)
HallC5×C7 ⋊ C3⋊AGL(1,𝔽13)
SylowC13 ⋊ C5×C3⋊(ΓL(1,𝔽8)⋊C4)
SylowC7 ⋊ C5×C3⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#11763985
commutator, hypocenterC3×C7×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×#10587716C2
cosocleC3×C7×D13C2×C3×C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

112 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 36 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) = 1365

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 438);