Finite Group Databasebeta

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C5×C11×A4×C47 #44526682

order31020
automorphism?
homologyAbelianization (H1) = C3×C5×C11×C47 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×A4×C47
unambiguous semidirect productC22⋊(C3×C5×C11×C47)
unambiguous semidirect product(C22×C5)⋊(C3×C11×C47)
unambiguous semidirect product(C22×C47)⋊(C3×C5×C11)
unambiguous semidirect product(C22×C5×C11)⋊(C3×C47)
unambiguous semidirect product(C22×C5×C47)⋊(C3×C11)
unambiguous semidirect product(C22×C5×C11×C47)⋊C3

Splittings

Fitting, socle, HallC22×C5×C11×C47 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C11×C47
HallC22×C11×C47 ⋊ C3×C5
HallC22×C5×C47 ⋊ C3×C11
HallC22×C5×C11 ⋊ C3×C47
HallC22×C47 ⋊ C3×C5×C11
HallC22×C11 ⋊ C3×C5×C47
HallC22×C5 ⋊ C3×C11×C47

Subgroups

subgroupG/H
center, hypercenterC5×C11×C47A4
commutator, cosocle, hypocenterC22C3×C5×C11×C47
FrattiniC1G
Fitting, socleC22×C5×C11×C47C3
LCSG ▷ C22
UCSC1 ◁ C5×C11×C47

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10340

Conjugacy classes & character table

10340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 85);