Finite Group Databasebeta

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C7×D11×D19⋊C3 #31798235

order17556
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D11×D19⋊C3
unambiguous semidirect productD19⋊(C3×C7×D11)
unambiguous semidirect product(D11×D19)⋊(C3×C7)
unambiguous semidirect product(C11×D19⋊C3)⋊(C2×C7)
unambiguous semidirect product(D11×C19⋊C3)⋊(C2×C7)
unambiguous semidirect product(C11⋊(D19⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C22×C3
derived, HallC11×C19 ⋊ C22×C3×C7
HallC7×D11×D19 ⋊ C3
HallC7×C11×C19⋊C3 ⋊ C22
HallD11×D19 ⋊ C3×C7
HallC11×C19⋊C3 ⋊ C22×C7
HallC7×C19⋊C3 ⋊ C2×D11
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×C7×D11
SylowC19 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C7×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D11×D19⋊C3
commutator, cosocle, hypocenterC11×C19C22×C3×C7
FrattiniC1G
Fitting, socleC7×C11×C19C22×C3
LCSG ▷ C11×C19
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 50);