Finite Group Databasebeta

← Prev (#31798337) Next (#31798339) →

C2×C11×C19×D21 #31798338

order17556
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C11×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C19×D21
unambiguous semidirect product(C2×C3)⋊(C11×D7×C19)
unambiguous semidirect product(C2×C7)⋊(D3×C11×C19)

Splittings

Fitting, socleC2×C3×C7×C11×C19 ⋊ C2
derived, HallC3×C7 ⋊ C22×C11×C19
HallC3×C7×C11×C19 ⋊ C22
HallC7×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D7
HallC3×C7×C19 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C19
HallC7×C19 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D3×C19
HallC3×C19 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×D7×C19
SylowC7 ⋊ C2×D3×C11×C19
SylowC3 ⋊ C2×C11×D7×C19

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D21
commutator, cosocle, hypocenterC3×C7C22×C11×C19
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C19C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C11×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8778

Conjugacy classes & character table

5016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 153);