Finite Group Databasebeta

← Prev (#30685825) Next (#30685827) →

C2×C3×C52×D19⋊C3 #30685826

order17100
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×C52×D19⋊C3
unambiguous semidirect productD19⋊(C2×C32×C52)
unambiguous semidirect product(C19⋊C3)⋊(C22×C3×C52)
unambiguous semidirect product(C2×D19)⋊(C32×C52)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C3×C52)
unambiguous semidirect product(C2×C3×D19)⋊(C3×C52)
unambiguous semidirect product(C2×C5×D19)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C5×D19)⋊(C3×C5)

Splittings

Fitting, socleC2×C3×C52×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C32×C52
HallC3×C52×C19⋊C3 ⋊ C22
HallC2×C52×D19 ⋊ C32
HallC52×C19 ⋊ C22×C32
HallC3×C19⋊C3 ⋊ C22×C52
HallC2×D19 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D19⋊C3
commutator, cosocle, hypocenterC19C22×C32×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C2×C3×C52

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2850

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 463);