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C5×D3×D319 #34062378

order19140
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D319
unambiguous semidirect product(D3×C29)⋊(C5×D11)

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C22
derived, HallC3×C11×C29 ⋊ C22×C5
HallC5×C11×C29 ⋊ C2×D3
HallC3×C5×C29 ⋊ C2×D11
HallC11×C29 ⋊ C2×C5×D3
HallC3×C5×C11 ⋊ C2×D29
HallC5×C29 ⋊ D3×D11
HallC3×C29 ⋊ C2×C5×D11
HallC5×C11 ⋊ D3×D29
HallC3×C11 ⋊ C2×C5×D29
SylowC29 ⋊ C5×D3×D11
HallC3×C5 ⋊ C2×D319
SylowC11 ⋊ C5×D3×D29
SylowC3 ⋊ C2×C5×D319

Subgroups

subgroupG/H
center, hypercenterC5D3×D319
commutator, cosocle, hypocenterC3×C11×C29C22×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C29C22
LCSG ▷ C3×C11×C29
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

2415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 71);