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C49×C3⋊(D13⋊C3) #26039400

order11466
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×C3⋊(D13⋊C3)
unambiguous semidirect productC3⋊(C49×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D3×C49)
unambiguous semidirect productD39⋊(C3×C49)

Splittings

FittingC3×C13×C49 ⋊ C2×C3
derivedC3×C13 ⋊ C2×C3×C49
HallC3×C13⋊C3×C49 ⋊ C2
HallC13×C49 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C2×C49
SylowC13 ⋊ C3×D3×C49

Subgroups

subgroupG/H
center, hypercenterC49C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C2×C3×C49
FrattiniC7C7×C3⋊(D13⋊C3)
FittingC3×C13×C49C2×C3
socle, cosocleC3×C7×C13C2×C3×C7
prime radicalC7×C3⋊(D13⋊C3)C7
LCSG ▷ C3×C13
UCSC1 ◁ C49

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C49×D13⋊C3, D49×C3⋊(D13⋊C3), (C3⋊(D13⋊C3))⋊D49, …
maximal normal subgroup ofD3×C49×D13⋊C3, D49×C3⋊(D13⋊C3), (C3⋊(D13⋊C3))⋊D49, …
maximal quotient ofC49×C3⋊(Dic13⋊C3), C2×C49×C3⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 43);