Finite Group Databasebeta

← Prev (#37587794) Next (#37587796) →

C43×C5⋊(D19⋊C3) #37587795

order24510
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C43×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C43)
unambiguous semidirect productD95⋊(C3×C43)

Splittings

Fitting, socle, HallC5×C19×C43 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C43
HallC5×C43×C19⋊C3 ⋊ C2
HallC43×D95 ⋊ C3
HallC43×C19⋊C3 ⋊ D5
HallC19×C43 ⋊ C3×D5
HallC5×C19⋊C3 ⋊ C2×C43
HallC5×C43 ⋊ D19⋊C3
HallD95 ⋊ C3×C43
HallC19⋊C3 ⋊ D5×C43
SylowC19 ⋊ C3×D5×C43
SylowC5 ⋊ C43×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC43C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C19C2×C3×C43
FrattiniC1G
Fitting, socleC5×C19×C43C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4085

Conjugacy classes & character table

1161 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 42);