Finite Group Databasebeta

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C3×C7×D705 #44444117

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

Aliases

direct productC3×C7×D705
unambiguous semidirect productC3⋊(C3×C7×D235)
unambiguous semidirect productC5⋊(C3×C7×D141)
unambiguous semidirect productC47⋊(C3×C7×D15)

Splittings

Fitting, socle, HallC32×C5×C7×C47 ⋊ C2
derivedC3×C5×C47 ⋊ C2×C3×C7
HallC32×C7×C47 ⋊ D5
HallC32×C5×C47 ⋊ C2×C7
HallC5×C7×C47 ⋊ C3×D3
HallC32×C47 ⋊ C7×D5
HallC7×C47 ⋊ C3×D15
HallC32×C5×C7 ⋊ D47
HallC5×C47 ⋊ C3×D3×C7
HallC32×C7 ⋊ D235
SylowC47 ⋊ C3×C7×D15
HallC32×C5 ⋊ C7×D47
HallC5×C7 ⋊ C3×D141
SylowC32 ⋊ C7×D235
SylowC5 ⋊ C3×C7×D141

Subgroups

subgroupG/H
center, hypercenterC3×C7D705
commutator, cosocle, hypocenterC3×C5×C47C2×C3×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C3×C5×C47
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9870

Conjugacy classes & character table

7434 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 54);