Finite Group Databasebeta

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C11×D19×D21 #31798304

order17556
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D19×D21
unambiguous semidirect product(C3×D19)⋊(C11×D7)
unambiguous semidirect product(C7×D19)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C22
derived, HallC3×C7×C19 ⋊ C22×C11
HallC7×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D7
HallC3×C7×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×D21
HallC7×C19 ⋊ C2×D3×C11
HallC7×C11 ⋊ D3×D19
HallC3×C19 ⋊ C2×C11×D7
HallC3×C11 ⋊ D7×D19
HallC3×C7 ⋊ C2×C11×D19
SylowC19 ⋊ C2×C11×D21
SylowC7 ⋊ D3×C11×D19
SylowC3 ⋊ C11×D7×D19

Subgroups

subgroupG/H
center, hypercenterC11D19×D21
commutator, cosocle, hypocenterC3×C7×C19C22×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C19C22
LCSG ▷ C3×C7×C19
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 119);