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C3⋊(C5⋊D665) #34093103

order19950
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC3⋊(C5⋊D665)
unambiguous semidirect productC5⋊D1995
unambiguous semidirect productC7⋊(C3⋊(C5⋊D95))
unambiguous semidirect productC19⋊(C3⋊(C5⋊D35))

Splittings

Fitting, socle, derived, HallC3×C52×C7×C19 ⋊ C2
HallC52×C7×C19 ⋊ D3
HallC3×C52×C19 ⋊ D7
HallC3×C52×C7 ⋊ D19
HallC52×C19 ⋊ D21
HallC3×C7×C19 ⋊ C5⋊D5
HallC52×C7 ⋊ D57
HallC7×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ D133
HallC3×C19 ⋊ C5⋊D35
SylowC52 ⋊ D399
HallC3×C7 ⋊ C5⋊D95
SylowC19 ⋊ C3⋊(C5⋊D35)
SylowC7 ⋊ C3⋊(C5⋊D95)
SylowC3 ⋊ C5⋊D665

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C19C2
LCSG ▷ C3×C52×C7×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9975

Polycyclic presentation:

2,3,5^2,7,19|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^18

Conjugacy classes & character table

4989 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 142);