Finite Group Databasebeta

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C13×C25⋊(D19⋊C3) #49150211

order37050
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25⋊(D19⋊C3)
unambiguous semidirect productC25⋊(C13×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C13×D25)
unambiguous semidirect productD475⋊(C3×C13)

Splittings

Fitting, HallC13×C19×C25 ⋊ C2×C3
derived, HallC19×C25 ⋊ C2×C3×C13
HallC13×C25×C19⋊C3 ⋊ C2
HallC13×D475 ⋊ C3
HallC25×C19⋊C3 ⋊ C2×C13
HallD475 ⋊ C3×C13
HallC13×C19⋊C3 ⋊ D25
HallC13×C25 ⋊ D19⋊C3
HallC13×C19 ⋊ C3×D25
HallC19⋊C3 ⋊ C13×D25
SylowC25 ⋊ C13×D19⋊C3
SylowC19 ⋊ C3×C13×D25

Subgroups

subgroupG/H
center, hypercenterC13C25⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C25C2×C3×C13
FrattiniC5C13×C5⋊(D19⋊C3)
FittingC13×C19×C25C2×C3
socleC5×C13×C19C3×D5
LCSG ▷ C19×C25
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1521 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 37);