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D19⋊C3×D31⋊C5 #47977604

order35340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productD19⋊C3×D31⋊C5
unambiguous semidirect productD19⋊(C3×D31⋊C5)
unambiguous semidirect product(D31×D19⋊C3)⋊C5
unambiguous semidirect product(C19⋊C3×D31⋊C5)⋊C2
unambiguous semidirect product(D19⋊C3×ΓL(1,𝔽32))⋊C2
unambiguous semidirect product((C19⋊C3)⋊(D31⋊C5))⋊C2

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C22×C3×C5
HallD19×D31⋊C5 ⋊ C3
HallC19⋊C3×ΓL(1,𝔽32) ⋊ C22
HallD31×D19⋊C3 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C22×C3
HallD19×D31 ⋊ C3×C5
HallC31×C19⋊C3 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×D19⋊C3
HallC19⋊C3 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C2×C3×D31⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C31C22×C3×C5
LCSG ▷ C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 589

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 76);