Finite Group Databasebeta

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C3×D3315 #34091065

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

Aliases

direct productC3×D3315
unambiguous semidirect productC3⋊(C3×D1105)
unambiguous semidirect productC5⋊(C3×D663)
unambiguous semidirect productC17⋊(C3×D195)

Splittings

Fitting, socle, HallC32×C5×C13×C17 ⋊ C2
derivedC3×C5×C13×C17 ⋊ C2×C3
HallC32×C13×C17 ⋊ D5
HallC5×C13×C17 ⋊ C3×D3
HallC32×C5×C17 ⋊ D13
HallC32×C5×C13 ⋊ D17
HallC13×C17 ⋊ C3×D15
HallC32×C17 ⋊ D65
HallC32×C13 ⋊ D85
HallC5×C17 ⋊ C3×D39
HallC5×C13 ⋊ C3×D51
HallC32×C5 ⋊ D221
SylowC17 ⋊ C3×D195
SylowC13 ⋊ C3×D255
SylowC32 ⋊ D1105
SylowC5 ⋊ C3×D663

Subgroups

subgroupG/H
center, hypercenterC3D3315
commutator, cosocle, hypocenterC3×C5×C13×C17C2×C3
FrattiniC1G
Fitting, socleC32×C5×C13×C17C2
LCSG ▷ C3×C5×C13×C17
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6630

Conjugacy classes & character table

4977 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 50);