Finite Group Databasebeta

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C3×C5×C17×D39 #34091070

order19890
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C17×D39
unambiguous semidirect productC3⋊(C3×C5×C17×D13)

Splittings

Fitting, socle, HallC32×C5×C13×C17 ⋊ C2
derivedC3×C13 ⋊ C2×C3×C5×C17
HallC32×C13×C17 ⋊ C2×C5
HallC5×C13×C17 ⋊ C3×D3
HallC32×C5×C17 ⋊ D13
HallC32×C5×C13 ⋊ C2×C17
HallC13×C17 ⋊ C3×C5×D3
HallC32×C17 ⋊ C5×D13
HallC32×C13 ⋊ C2×C5×C17
HallC5×C13 ⋊ C3×D3×C17
HallC32×C5 ⋊ C17×D13
SylowC13 ⋊ C3×C5×D3×C17
SylowC32 ⋊ C5×C17×D13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C17D39
commutator, cosocle, hypocenterC3×C13C2×C3×C5×C17
FrattiniC1G
Fitting, socleC32×C5×C13×C17C2
LCSG ▷ C3×C13
UCSC1 ◁ C3×C5×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

5355 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 55);