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C3×(C13⋊C3)⋊D47 #24926957

order10998
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C13⋊C3)⋊D47
unambiguous semidirect product(C13⋊C3)⋊(C3×D47)
unambiguous semidirect productC47⋊(C3×D13⋊C3)
unambiguous semidirect productD611⋊C32
unambiguous semidirect product(C3×D611)⋊C3

Splittings

Fitting, socleC3×C13×C47 ⋊ C2×C3
derived, HallC13×C47 ⋊ C2×C32
HallC3×C13⋊C3×C47 ⋊ C2
HallD611 ⋊ C32
HallC3×C13⋊C3 ⋊ D47
SylowC47 ⋊ C3×D13⋊C3
SylowC13 ⋊ C32×D47

Subgroups

subgroupG/H
center, hypercenterC3(C13⋊C3)⋊D47
commutator, cosocle, hypocenterC13×C47C2×C32
FrattiniC1G
Fitting, socleC3×C13×C47C2×C3
LCSG ▷ C13×C47
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

507 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D13⋊C3×D47, D3×(C13⋊C3)⋊D47, (C3⋊(D13⋊C3))⋊D47, …
maximal normal subgroup ofC3×D13⋊C3×D47, D3×(C13⋊C3)⋊D47, (C3⋊(D13⋊C3))⋊D47, …
maximal quotient ofC3×C47⋊(Dic13⋊C3), C2×C3×(C13⋊C3)⋊D47

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10998, 15);