Finite Group Databasebeta

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C3×C3⋊(C19⋊#1035) #30685489

order17100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC32×C19×C25 ⋊ C4
derivedC3×C19×C25 ⋊ C3×C4
HallC19×C25 ⋊ C3×Dic3
HallC32×C25 ⋊ Dic19
HallC32×C19 ⋊ #1035
SylowC25 ⋊ C3×Dic57
SylowC19 ⋊ C3×C3⋊#1035
SylowC32 ⋊ C19⋊#1035

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C19⋊#1035)
commutator, hypocenterC3×C19×C25C3×C4
FrattiniC5C3×C3⋊(C19⋊AGL(1,𝔽5))
FittingC32×C19×C25C4
socleC32×C5×C19AGL(1,𝔽5)
prime radicalC32×C19×D25C2
cosocleC3×C19×D25C2×C3
LCSG ▷ C3×C19×C25
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2850

Conjugacy classes & character table

1206 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 126);