Finite Group Databasebeta

← Prev (#49175807) Next (#49175809) →

C7×C47×D19⋊C3 #49175808

order37506
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C47 · Schur multiplier (H2) = C1

Aliases

direct productC7×C47×D19⋊C3
unambiguous semidirect productD19⋊(C3×C7×C47)
unambiguous semidirect product(C19⋊C3)⋊(C2×C7×C47)
unambiguous semidirect product(D19×C47)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C19×C47 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C7×C47
HallC7×C47×C19⋊C3 ⋊ C2
HallC7×D19×C47 ⋊ C3
HallC47×C19⋊C3 ⋊ C2×C7
HallD19×C47 ⋊ C3×C7
HallC19×C47 ⋊ C2×C3×C7
HallC7×C19⋊C3 ⋊ C2×C47
HallC7×D19 ⋊ C3×C47
HallC7×C19 ⋊ C2×C3×C47
HallC19⋊C3 ⋊ C2×C7×C47
HallD19 ⋊ C3×C7×C47

Subgroups

subgroupG/H
center, hypercenterC7×C47D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C7×C47
FrattiniC1G
Fitting, socleC7×C19×C47C2×C3
LCSG ▷ C19
UCSC1 ◁ C7×C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6251

Conjugacy classes & character table

2961 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37506, 25);