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C19×C3⋊(C5⋊D35) #34093104

order19950
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C5

Aliases

direct productC19×C3⋊(C5⋊D35)
unambiguous semidirect productC3⋊(C19×C5⋊D35)
unambiguous semidirect productC5⋊(C19×D105)
unambiguous semidirect productC7⋊(C19×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C7×C19 ⋊ C2
derived, HallC3×C52×C7 ⋊ C2×C19
HallC52×C7×C19 ⋊ D3
HallC3×C52×C19 ⋊ D7
HallC52×C19 ⋊ D21
HallC3×C7×C19 ⋊ C5⋊D5
HallC52×C7 ⋊ D3×C19
HallC7×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ D7×C19
HallC3×C19 ⋊ C5⋊D35
SylowC52 ⋊ C19×D21
HallC3×C7 ⋊ C19×C5⋊D5
SylowC7 ⋊ C19×C3⋊(C5⋊D5)
SylowC3 ⋊ C19×C5⋊D35

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C5⋊D35)
commutator, cosocle, hypocenterC3×C52×C7C2×C19
FrattiniC1G
Fitting, socleC3×C52×C7×C19C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9975

Conjugacy classes & character table

5016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 143);