Finite Group Databasebeta

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C3×C5×D987 #44444115

order29610
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D987
unambiguous semidirect productC3⋊(C3×C5×D329)
unambiguous semidirect productC47⋊(C3×C5×D21)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derivedC3×C7×C47 ⋊ C2×C3×C5
HallC32×C7×C47 ⋊ C2×C5
HallC32×C5×C47 ⋊ D7
HallC5×C7×C47 ⋊ C3×D3
HallC32×C47 ⋊ C5×D7
HallC7×C47 ⋊ C3×C5×D3
HallC32×C5×C7 ⋊ D47
HallC5×C47 ⋊ C3×D21
HallC32×C7 ⋊ C5×D47
SylowC47 ⋊ C3×C5×D21
HallC32×C5 ⋊ D329
HallC5×C7 ⋊ C3×D141
SylowC32 ⋊ C5×D329
SylowC7 ⋊ C3×C5×D141

Subgroups

subgroupG/H
center, hypercenterC3×C5D987
commutator, cosocle, hypocenterC3×C7×C47C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C3×C7×C47
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9870

Conjugacy classes & character table

7425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 52);