Finite Group Databasebeta

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C19⋊C3×D275 #44535459

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

Aliases

direct productC19⋊C3×D275
unambiguous semidirect productC11⋊(D25×C19⋊C3)
unambiguous semidirect productC25⋊(D11×C19⋊C3)
unambiguous semidirect product(C19×D275)⋊C3

Splittings

Fitting, derived, HallC11×C19×C25 ⋊ C2×C3
HallC11×C25×C19⋊C3 ⋊ C2
HallC19×D275 ⋊ C3
HallC25×C19⋊C3 ⋊ D11
HallC11×C19⋊C3 ⋊ D25
HallC19×C25 ⋊ C3×D11
HallC11×C25 ⋊ C2×C19⋊C3
HallC11×C19 ⋊ C3×D25
SylowC25 ⋊ D11×C19⋊C3
SylowC19 ⋊ C3×D275
SylowC11 ⋊ D25×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C19×C25C2×C3
FrattiniC5C19⋊C3×D55
socleC5×C11×C19C3×D5
LCSG ▷ C11×C19×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

1251 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 32);