Finite Group Databasebeta

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C5×D51⋊D19 #34084366

order19380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D51⋊D19
unambiguous semidirect productD51⋊(C5×D19)
unambiguous semidirect productD57⋊(C5×D17)
unambiguous semidirect productD323⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C17×C19 ⋊ C22
derived, HallC3×C17×C19 ⋊ C22×C5
HallC5×C17×C19 ⋊ C2×D3
HallC17×C19 ⋊ C2×C5×D3
HallC3×C5×C19 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D19
HallC5×C19 ⋊ D3×D17
HallC5×C17 ⋊ D3×D19
HallC3×C19 ⋊ C2×C5×D17
HallC3×C17 ⋊ C2×C5×D19
SylowC19 ⋊ C5×D3×D17
SylowC17 ⋊ C5×D3×D19
HallC3×C5 ⋊ D17×D19
SylowC3 ⋊ C5×D17×D19

Subgroups

subgroupG/H
center, hypercenterC5D51⋊D19
commutator, cosocle, hypocenterC3×C17×C19C22×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C19C22
LCSG ▷ C3×C17×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4845

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 78);