Finite Group Databasebeta

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C11×C25⋊(D19⋊C3) #44535458

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25⋊(D19⋊C3)
unambiguous semidirect productC25⋊(C11×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C11×D25)
unambiguous semidirect productD475⋊(C3×C11)
unambiguous semidirect product(C11×D475)⋊C3

Splittings

Fitting, HallC11×C19×C25 ⋊ C2×C3
derived, HallC19×C25 ⋊ C2×C3×C11
HallC11×C25×C19⋊C3 ⋊ C2
HallC11×D475 ⋊ C3
HallC25×C19⋊C3 ⋊ C2×C11
HallD475 ⋊ C3×C11
HallC11×C19⋊C3 ⋊ D25
HallC11×C25 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×D25
HallC19⋊C3 ⋊ C11×D25
SylowC25 ⋊ C11×D19⋊C3
SylowC19 ⋊ C3×C11×D25

Subgroups

subgroupG/H
center, hypercenterC11C25⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C25C2×C3×C11
FrattiniC5C11×C5⋊(D19⋊C3)
FittingC11×C19×C25C2×C3
socleC5×C11×C19C3×D5
LCSG ▷ C19×C25
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 31);