Finite Group Databasebeta

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C5×C7×C3⋊D141 #44444121

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

Aliases

direct productC5×C7×C3⋊D141
unambiguous semidirect productC3⋊(C5×C7×D141)
unambiguous semidirect productC47⋊(C5×C7×C3⋊D3)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D141
commutator, cosocle, hypocenterC32×C47C2×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C47C2
LCSG ▷ C32×C47
UCSC1 ◁ C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14805

Conjugacy classes & character table

7455 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 58);