Finite Group Databasebeta

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C3×D3255 #34086297

order19530
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3255
unambiguous semidirect productC3⋊(C3×D1085)
unambiguous semidirect productC5⋊(C3×D651)

Splittings

Fitting, socle, HallC32×C5×C7×C31 ⋊ C2
derivedC3×C5×C7×C31 ⋊ C2×C3
HallC32×C7×C31 ⋊ D5
HallC32×C5×C31 ⋊ D7
HallC5×C7×C31 ⋊ C3×D3
HallC32×C5×C7 ⋊ D31
HallC32×C31 ⋊ D35
HallC7×C31 ⋊ C3×D15
HallC5×C31 ⋊ C3×D21
HallC32×C7 ⋊ D155
HallC32×C5 ⋊ D217
HallC5×C7 ⋊ C3×D93
SylowC31 ⋊ C3×D105
SylowC32 ⋊ D1085
SylowC7 ⋊ C3×D465
SylowC5 ⋊ C3×D651

Subgroups

subgroupG/H
center, hypercenterC3D3255
commutator, cosocle, hypocenterC3×C5×C7×C31C2×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C31C2
LCSG ▷ C3×C5×C7×C31
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6510

Conjugacy classes & character table

4887 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 202);