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C19×C3⋊(C5⋊D65) #49150337

order37050
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C5

Aliases

direct productC19×C3⋊(C5⋊D65)
unambiguous semidirect productC3⋊(C19×C5⋊D65)
unambiguous semidirect productC5⋊(C19×D195)
unambiguous semidirect productC13⋊(C19×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C13×C19 ⋊ C2
derived, HallC3×C52×C13 ⋊ C2×C19
HallC52×C13×C19 ⋊ D3
HallC3×C52×C19 ⋊ D13
HallC3×C13×C19 ⋊ C5⋊D5
HallC52×C19 ⋊ D39
HallC52×C13 ⋊ D3×C19
HallC13×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C19×D13
HallC3×C19 ⋊ C5⋊D65
HallC3×C13 ⋊ C19×C5⋊D5
SylowC52 ⋊ C19×D39
SylowC13 ⋊ C19×C3⋊(C5⋊D5)
SylowC3 ⋊ C19×C5⋊D65

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C5⋊D65)
commutator, cosocle, hypocenterC3×C52×C13C2×C19
FrattiniC1G
Fitting, socleC3×C52×C13×C19C2
LCSG ▷ C3×C52×C13
UCSC1 ◁ C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18525

Conjugacy classes & character table

9291 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 163);