Finite Group Databasebeta

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C3×C47×D105 #44444118

order29610
automorphism?
homologyAbelianization (H1) = C2×C3×C47 · Schur multiplier (H2) = C1

Aliases

direct productC3×C47×D105
unambiguous semidirect productC3⋊(C3×C47×D35)
unambiguous semidirect productC5⋊(C3×D21×C47)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derivedC3×C5×C7 ⋊ C2×C3×C47
HallC32×C7×C47 ⋊ D5
HallC32×C5×C47 ⋊ D7
HallC5×C7×C47 ⋊ C3×D3
HallC32×C47 ⋊ D35
HallC7×C47 ⋊ C3×D15
HallC32×C5×C7 ⋊ C2×C47
HallC5×C47 ⋊ C3×D21
HallC32×C7 ⋊ D5×C47
HallC32×C5 ⋊ D7×C47
HallC5×C7 ⋊ C3×D3×C47
SylowC32 ⋊ C47×D35
SylowC7 ⋊ C3×D15×C47
SylowC5 ⋊ C3×D21×C47

Subgroups

subgroupG/H
center, hypercenterC3×C47D105
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C47
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C47

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9870

Conjugacy classes & character table

7614 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 55);