Finite Group Databasebeta

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D3×C7×D209 #31798302

order17556
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D209
unambiguous semidirect product(D3×C11)⋊(C7×D19)
unambiguous semidirect product(D3×C19)⋊(C7×D11)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C22
derived, HallC3×C11×C19 ⋊ C22×C7
HallC7×C11×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×D3×C7
HallC7×C19 ⋊ D3×D11
HallC7×C11 ⋊ D3×D19
HallC3×C19 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D19
HallC3×C7 ⋊ C2×D209
SylowC19 ⋊ D3×C7×D11
SylowC11 ⋊ D3×C7×D19
SylowC3 ⋊ C2×C7×D209

Subgroups

subgroupG/H
center, hypercenterC7D3×D209
commutator, cosocle, hypocenterC3×C11×C19C22×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C19C22
LCSG ▷ C3×C11×C19
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

2226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 117);