Finite Group Databasebeta

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C3×(C19⋊C3)⋊#1035 #30685463

order17100
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C19⋊C3)⋊#1035
unambiguous semidirect product(C19⋊C3)⋊(C3×#1035)
unambiguous semidirect product(C19⋊#1035)⋊C32
unambiguous semidirect product(C3×C19⋊#1035)⋊C3

Splittings

FittingC3×C19×C25 ⋊ C3×C4
derived, HallC19×C25 ⋊ C32×C4
HallC3×C25×C19⋊C3 ⋊ C4
HallC19⋊#1035 ⋊ C32
HallC3×C19⋊C3 ⋊ #1035
SylowC25 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×#1035

Subgroups

subgroupG/H
center, hypercenterC3(C19⋊C3)⋊#1035
commutator, hypocenterC19×C25C32×C4
FrattiniC5C3×(C19⋊C3)⋊AGL(1,𝔽5)
FittingC3×C19×C25C3×C4
socleC3×C5×C19C3×AGL(1,𝔽5)
prime radicalC3×D25×C19⋊C3C2
cosocleC19×D25C2×C32
LCSG ▷ C19×C25
UCSC1 ◁ C3

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1425

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 100);