Finite Group Databasebeta

← Prev (#44444112) Next (#44444114) →

C3×C5×C7×D141 #44444113

order29610
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×D141
unambiguous semidirect productC3⋊(C3×C5×C7×D47)
unambiguous semidirect productC47⋊(C3×C5×D3×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derivedC3×C47 ⋊ C2×C3×C5×C7
HallC32×C7×C47 ⋊ C2×C5
HallC32×C5×C47 ⋊ C2×C7
HallC5×C7×C47 ⋊ C3×D3
HallC32×C47 ⋊ C2×C5×C7
HallC7×C47 ⋊ C3×C5×D3
HallC32×C5×C7 ⋊ D47
HallC5×C47 ⋊ C3×D3×C7
HallC32×C7 ⋊ C5×D47
SylowC47 ⋊ C3×C5×D3×C7
HallC32×C5 ⋊ C7×D47
SylowC32 ⋊ C5×C7×D47

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7D141
commutator, cosocle, hypocenterC3×C47C2×C3×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C3×C47
UCSC1 ◁ C3×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9870

Conjugacy classes & character table

7560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 50);