Finite Group Databasebeta

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C2×C47×D165 #44526696

order31020
automorphism?
homologyAbelianization (H1) = C22×C47 · Schur multiplier (H2) = C2

Aliases

direct productC2×C47×D165
unambiguous semidirect product(C2×C3)⋊(C47×D55)
unambiguous semidirect product(C2×C5)⋊(C47×D33)
unambiguous semidirect product(C2×C11)⋊(D15×C47)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC3×C5×C11 ⋊ C22×C47
HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C2×D3
HallC3×C11×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D11
HallC11×C47 ⋊ C2×D15
HallC5×C47 ⋊ C2×D33
HallC3×C47 ⋊ C2×D55
HallC5×C11 ⋊ C2×D3×C47
HallC3×C11 ⋊ C2×D5×C47
HallC3×C5 ⋊ C2×D11×C47
SylowC11 ⋊ C2×D15×C47
SylowC5 ⋊ C2×C47×D33
SylowC3 ⋊ C2×C47×D55

Subgroups

subgroupG/H
center, hypercenterC2×C47D165
commutator, cosocle, hypocenterC3×C5×C11C22×C47
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C47

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15510

Conjugacy classes & character table

7896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 99);