Finite Group Databasebeta

← Prev (#28414898) Next (#28414900) →

C19×C3⋊#63121 #28414899

order14820
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C3⋊#63121
unambiguous semidirect productC3⋊(C19×#63121)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C19
HallC5×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ #261
HallC13×C19 ⋊ ΓL(1,𝔽16)
HallC5×C19 ⋊ C3⋊#261
HallC5×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ #63121
HallC3×C13 ⋊ C19×AGL(1,𝔽5)
HallC3×C5 ⋊ C19×#261
SylowC13 ⋊ C19×ΓL(1,𝔽16)
SylowC5 ⋊ C19×C3⋊#261
SylowC3 ⋊ C19×#63121

Subgroups

subgroupG/H
center, hypercenterC19C3⋊#63121
commutator, hypocenterC3×C5×C13C4×C19
FrattiniC1G
Fitting, socleC3×C5×C13×C19C4
prime radicalC3×C19×D65C2
cosocleC3×D65C2×C19
LCSG ▷ C3×C5×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1026 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 185);