Finite Group Databasebeta

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D5×C11⋊C5×C19⋊C3 #44535471

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11⋊C5×C19⋊C3
unambiguous semidirect productC5⋊(C2×C11⋊C5×C19⋊C3)
unambiguous semidirect product(D5×C11)⋊(C5×C19⋊C3)
unambiguous semidirect product(D5×C19)⋊(C3×C11⋊C5)
unambiguous semidirect product(D5×C11×C19⋊C3)⋊C5
unambiguous semidirect product(D5×C19×C11⋊C5)⋊C3

Splittings

Fitting, socle, derivedC5×C11×C19 ⋊ C2×C3×C5
HallC5×C11⋊C5×C19⋊C3 ⋊ C2
HallD5×C19×C11⋊C5 ⋊ C3
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC11×C19⋊C3 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C19⋊C3
HallC11×C19 ⋊ C3×C5×D5
SylowC19 ⋊ C3×D5×C11⋊C5
SylowC11 ⋊ C5×D5×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C19C2×C3×C5
LCSG ▷ C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1045

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 44);