Finite Group Databasebeta

← Prev (#37587789) Next (#37587791) →

C19×C5⋊(D43⋊C3) #37587790

order24510
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C5⋊(D43⋊C3)
unambiguous semidirect productC5⋊(C19×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(D5×C19)
unambiguous semidirect productD215⋊(C3×C19)

Splittings

Fitting, socle, HallC5×C19×C43 ⋊ C2×C3
derived, HallC5×C43 ⋊ C2×C3×C19
HallC5×C19×C43⋊C3 ⋊ C2
HallC19×D215 ⋊ C3
HallC19×C43⋊C3 ⋊ D5
HallC19×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ C2×C19
HallD215 ⋊ C3×C19
HallC43⋊C3 ⋊ D5×C19
HallC5×C19 ⋊ D43⋊C3
SylowC43 ⋊ C3×D5×C19
SylowC5 ⋊ C19×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC19C5⋊(D43⋊C3)
commutator, cosocle, hypocenterC5×C43C2×C3×C19
FrattiniC1G
Fitting, socleC5×C19×C43C2×C3
LCSG ▷ C5×C43
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4085

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 37);