Finite Group Databasebeta

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C2×C3×C47×D55 #44526688

order31020
automorphism?
homologyAbelianization (H1) = C22×C3×C47 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C47×D55
unambiguous semidirect product(C2×C5)⋊(C3×D11×C47)
unambiguous semidirect product(C2×C11)⋊(C3×D5×C47)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC5×C11 ⋊ C22×C3×C47
HallC3×C5×C11×C47 ⋊ C22
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 ⋊ C22×C47
HallC3×C11 ⋊ C2×D5×C47
HallC3×C5 ⋊ C2×D11×C47
SylowC11 ⋊ C2×C3×D5×C47
SylowC5 ⋊ C2×C3×D11×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C47D55
commutator, cosocle, hypocenterC5×C11C22×C3×C47
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C47

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15510

Conjugacy classes & character table

8178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 91);