Finite Group Databasebeta

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C5×D19×D39 #28414890

order14820
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D19×D39
unambiguous semidirect product(C3×D19)⋊(C5×D13)
unambiguous semidirect product(C13×D19)⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C22
derived, HallC3×C13×C19 ⋊ C22×C5
HallC5×C13×C19 ⋊ C2×D3
HallC3×C5×C19 ⋊ C2×D13
HallC13×C19 ⋊ C2×C5×D3
HallC3×C5×C13 ⋊ C2×D19
HallC5×C19 ⋊ C2×D39
HallC5×C13 ⋊ D3×D19
HallC3×C19 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C5×D39
HallC3×C5 ⋊ D13×D19
SylowC13 ⋊ C5×D3×D19
SylowC3 ⋊ C5×D13×D19

Subgroups

subgroupG/H
center, hypercenterC5D19×D39
commutator, cosocle, hypocenterC3×C13×C19C22×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C19C22
LCSG ▷ C3×C13×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3705

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 176);