Finite Group Databasebeta

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C2×C3×D2585 #44526689

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

Aliases

direct productC2×C3×D2585
unambiguous semidirect product(C2×C5)⋊(C3×D517)
unambiguous semidirect product(C2×C11)⋊(C3×D235)
unambiguous semidirect product(C2×C47)⋊(C3×D55)

Splittings

Fitting, socleC2×C3×C5×C11×C47 ⋊ C2
derived, HallC5×C11×C47 ⋊ C22×C3
HallC3×C5×C11×C47 ⋊ C22
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 ⋊ C2×D55
HallC5×C11 ⋊ C2×C3×D47
SylowC47 ⋊ C2×C3×D55
HallC3×C11 ⋊ C2×D235
HallC3×C5 ⋊ C2×D517
SylowC11 ⋊ C2×C3×D235
SylowC5 ⋊ C2×C3×D517

Subgroups

subgroupG/H
center, hypercenterC2×C3D2585
commutator, cosocle, hypocenterC5×C11×C47C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C47C2
LCSG ▷ C5×C11×C47
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15510

Conjugacy classes & character table

7764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 92);