Finite Group Databasebeta

← Prev (#28414871) Next (#28414873) →

C3×C13×C19⋊AGL(1,𝔽5) #28414872

order14820
isoclinismisoclinic class of C19⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C19⋊AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C4
derived, HallC5×C19 ⋊ C3×C4×C13
HallC5×C13×C19 ⋊ C3×C4
HallC3×C13×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ C4×C13
HallC13×C19 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C13 ⋊ Dic19
HallC5×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ C13×AGL(1,𝔽5)
SylowC19 ⋊ C3×C13×AGL(1,𝔽5)
HallC3×C5 ⋊ C13×Dic19
SylowC5 ⋊ C3×C13×Dic19

Subgroups

subgroupG/H
center, hypercenterC3×C13C19⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C3×C4×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C19C4
prime radicalC3×D5×C13×C19C2
cosocleD5×C19C2×C3×C13
LCSG ▷ C5×C19
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1599 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 158);