Finite Group Databasebeta

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C5×(C19⋊C3)⋊(D19⋊C3) #44570514

order32490
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×(C19⋊C3)⋊(D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×D19⋊C3)
unambiguous semidirect product#14524207⋊(C3×C5)
unambiguous semidirect product((C19⋊C3)⋊D19)⋊(C3×C5)
unambiguous semidirect product(C5×#14524206)⋊C3
unambiguous semidirect product(C5×#14524207)⋊C3
unambiguous semidirect product(C5×(C19⋊C3)⋊D19)⋊C3

Splittings

Fitting, socle, HallC5×C192 ⋊ C2×C32
derived, SylowC192 ⋊ C2×C32×C5
HallC5×C19⋊C32 ⋊ C2
HallC5×C19⋊D19 ⋊ C32
HallC19⋊C32 ⋊ C2×C5
HallC19⋊D19 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC5(C19⋊C3)⋊(D19⋊C3)
commutator, cosocle, hypocenterC192C2×C32×C5
FrattiniC1G
Fitting, socleC5×C192C2×C32
LCSG ▷ C192
UCSC1 ◁ C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 285

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 98);