Finite Group Databasebeta

← Prev (#40999547) Next (#40999549) →

C5×C47⋊(D19⋊C3) #40999548

order26790
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C47⋊(D19⋊C3)
unambiguous semidirect productC47⋊(C5×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×D47)
unambiguous semidirect productD893⋊(C3×C5)
unambiguous semidirect product(C5×D893)⋊C3

Splittings

Fitting, socle, HallC5×C19×C47 ⋊ C2×C3
derived, HallC19×C47 ⋊ C2×C3×C5
HallC5×C47×C19⋊C3 ⋊ C2
HallC5×D893 ⋊ C3
HallC47×C19⋊C3 ⋊ C2×C5
HallD893 ⋊ C3×C5
HallC5×C19⋊C3 ⋊ D47
HallC5×C47 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D47
HallC19⋊C3 ⋊ C5×D47
SylowC47 ⋊ C5×D19⋊C3
SylowC19 ⋊ C3×C5×D47

Subgroups

subgroupG/H
center, hypercenterC5C47⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C47C2×C3×C5
FrattiniC1G
Fitting, socleC5×C19×C47C2×C3
LCSG ▷ C19×C47
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4465

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26790, 20);