Finite Group Databasebeta

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C2×C47×C5⋊(D13⋊C3) #49144028

order36660
automorphism?
homologyAbelianization (H1) = C22×C3×C47 · Schur multiplier (H2) = C2

Aliases

direct productC2×C47×C5⋊(D13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C47×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(D5×C47)
unambiguous semidirect product(C2×D65)⋊(C3×C47)
unambiguous semidirect product(C2×C47×D65)⋊C3

Splittings

Fitting, socleC2×C5×C13×C47 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C3×C47
HallC2×C47×D65 ⋊ C3
HallC5×C13⋊C3×C47 ⋊ C22
HallC5×C13×C47 ⋊ C22×C3
HallC13⋊C3×C47 ⋊ C2×D5
HallC13×C47 ⋊ C2×C3×D5
HallC2×D65 ⋊ C3×C47
HallC5×C47 ⋊ C2×D13⋊C3
HallC5×C13⋊C3 ⋊ C22×C47
HallC13⋊C3 ⋊ C2×D5×C47
SylowC13 ⋊ C2×C3×D5×C47
SylowC5 ⋊ C2×C47×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C47C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C22×C3×C47
FrattiniC1G
Fitting, socleC2×C5×C13×C47C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C47

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6110

Conjugacy classes & character table

2068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36660, 48);