Finite Group Databasebeta

← Prev (#11765894) Next (#11765896) →

C3⋊(C19⋊AGL(1,𝔽5)) #11765895

order1140
isoclinismisoclinic class of C3⋊(C19⋊AGL(1,𝔽5))
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC19⋊ΓL(1,𝔽16)

Splittings

Fitting, socle, derived, HallC3×C5×C19 ⋊ C4
HallC5×C19 ⋊ Dic3
HallC3×C19 ⋊ AGL(1,𝔽5)
SylowC19 ⋊ ΓL(1,𝔽16)
HallC3×C5 ⋊ Dic19
SylowC5 ⋊ Dic57
SylowC3 ⋊ C19⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C19C4
prime radical, cosocleC3×D5×C19C2
LCSG ▷ C3×C5×C19
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 285

Polycyclic presentation:

2^2,3,5,19|a^2=b,c^a=c^2,d^a=d^2,e^a=e^18,d^b=d^4

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊(C19⋊AGL(1,𝔽5)), C3⋊((C19⋊C3)⋊AGL(1,𝔽5)), C3×C3⋊(C19⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC3⋊((C19⋊C3)⋊AGL(1,𝔽5)), C3×C3⋊(C19⋊AGL(1,𝔽5)), C11×C3⋊(C19⋊AGL(1,𝔽5)), …
maximal quotient ofC9⋊(C19⋊AGL(1,𝔽5)), C3×C3⋊(C19⋊AGL(1,𝔽5)), C3⋊(C3⋊(C19⋊AGL(1,𝔽5))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1140, 23);