Finite Group Databasebeta

← Prev (#37587770) Next (#37587772) →

C19×D645 #37587771

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

Aliases

direct productC19×D645
unambiguous semidirect productC3⋊(C19×D215)
unambiguous semidirect productC5⋊(C19×D129)
unambiguous semidirect productC43⋊(C19×D15)

Splittings

Fitting, socle, HallC3×C5×C19×C43 ⋊ C2
derived, HallC3×C5×C43 ⋊ C2×C19
HallC5×C19×C43 ⋊ D3
HallC3×C19×C43 ⋊ D5
HallC19×C43 ⋊ D15
HallC3×C5×C19 ⋊ D43
HallC5×C43 ⋊ D3×C19
HallC3×C43 ⋊ D5×C19
HallC5×C19 ⋊ D129
HallC3×C19 ⋊ D215
SylowC43 ⋊ C19×D15
HallC3×C5 ⋊ C19×D43
SylowC5 ⋊ C19×D129
SylowC3 ⋊ C19×D215

Subgroups

subgroupG/H
center, hypercenterC19D645
commutator, cosocle, hypocenterC3×C5×C43C2×C19
FrattiniC1G
Fitting, socleC3×C5×C19×C43C2
LCSG ▷ C3×C5×C43
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12255

Conjugacy classes & character table

6156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 18);