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C3⋊(C5⋊D1235) #49150338

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

Aliases

unambiguous semidirect productC3⋊(C5⋊D1235)
unambiguous semidirect productC5⋊D3705
unambiguous semidirect productC13⋊(C3⋊(C5⋊D95))
unambiguous semidirect productC19⋊(C3⋊(C5⋊D65))

Splittings

Fitting, socle, derived, HallC3×C52×C13×C19 ⋊ C2
HallC52×C13×C19 ⋊ D3
HallC3×C52×C19 ⋊ D13
HallC3×C52×C13 ⋊ D19
HallC3×C13×C19 ⋊ C5⋊D5
HallC52×C19 ⋊ D39
HallC52×C13 ⋊ D57
HallC13×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ D247
HallC3×C19 ⋊ C5⋊D65
HallC3×C13 ⋊ C5⋊D95
SylowC52 ⋊ D741
SylowC19 ⋊ C3⋊(C5⋊D65)
SylowC13 ⋊ C3⋊(C5⋊D95)
SylowC3 ⋊ C5⋊D1235

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C13×C19C2
LCSG ▷ C3×C52×C13×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18525

Polycyclic presentation:

2,3,5^2,13,19|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^12,f^a=f^18

Conjugacy classes & character table

9264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 164);