Finite Group Databasebeta

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C3×C5×D663 #34091069

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

Aliases

direct productC3×C5×D663
unambiguous semidirect productC3⋊(C3×C5×D221)
unambiguous semidirect productC17⋊(C3×C5×D39)

Splittings

Fitting, socle, HallC32×C5×C13×C17 ⋊ C2
derivedC3×C13×C17 ⋊ C2×C3×C5
HallC32×C13×C17 ⋊ C2×C5
HallC5×C13×C17 ⋊ C3×D3
HallC32×C5×C17 ⋊ D13
HallC32×C5×C13 ⋊ D17
HallC13×C17 ⋊ C3×C5×D3
HallC32×C17 ⋊ C5×D13
HallC32×C13 ⋊ C5×D17
HallC5×C17 ⋊ C3×D39
HallC5×C13 ⋊ C3×D51
HallC32×C5 ⋊ D221
SylowC17 ⋊ C3×C5×D39
SylowC13 ⋊ C3×C5×D51
SylowC32 ⋊ C5×D221

Subgroups

subgroupG/H
center, hypercenterC3×C5D663
commutator, cosocle, hypocenterC3×C13×C17C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C13×C17C2
LCSG ▷ C3×C13×C17
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

4995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 54);