Finite Group Databasebeta

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C3×D55⋊D47 #44526649

order31020
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D55⋊D47
unambiguous semidirect productD55⋊(C3×D47)
unambiguous semidirect productD235⋊(C3×D11)
unambiguous semidirect productD517⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C5×C11×C47 ⋊ C22
derived, HallC5×C11×C47 ⋊ C22×C3
HallC3×C11×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×C3×D5
HallC5×C47 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ D5×D11
HallC5×C11 ⋊ C2×C3×D47
SylowC47 ⋊ C3×D5×D11
HallC3×C11 ⋊ D5×D47
HallC3×C5 ⋊ D11×D47
SylowC11 ⋊ C3×D5×D47
SylowC5 ⋊ C3×D11×D47

Subgroups

subgroupG/H
center, hypercenterC3D55⋊D47
commutator, cosocle, hypocenterC5×C11×C47C22×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C47C22
LCSG ▷ C5×C11×C47
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

2085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 52);