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C19×C3⋊(C5⋊D55) #44535542

order31350
automorphism?
homologyAbelianization (H1) = C2×C19 · Schur multiplier (H2) = C5

Aliases

direct productC19×C3⋊(C5⋊D55)
unambiguous semidirect productC3⋊(C19×C5⋊D55)
unambiguous semidirect productC5⋊(C19×D165)
unambiguous semidirect productC11⋊(C19×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derived, HallC3×C52×C11 ⋊ C2×C19
HallC52×C11×C19 ⋊ D3
HallC3×C52×C19 ⋊ D11
HallC3×C11×C19 ⋊ C5⋊D5
HallC52×C19 ⋊ D33
HallC52×C11 ⋊ D3×C19
HallC11×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C19×D11
HallC3×C19 ⋊ C5⋊D55
HallC3×C11 ⋊ C19×C5⋊D5
SylowC52 ⋊ C19×D33
SylowC11 ⋊ C19×C3⋊(C5⋊D5)
SylowC3 ⋊ C19×C5⋊D55

Subgroups

subgroupG/H
center, hypercenterC19C3⋊(C5⋊D55)
commutator, cosocle, hypocenterC3×C52×C11C2×C19
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C3×C52×C11
UCSC1 ◁ C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7866 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 115);