Finite Group Databasebeta

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C2×C3×C49×D19⋊C3 #45691387

order33516
automorphism?
homologyAbelianization (H1) = C22×C32×C49 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C49×D19⋊C3
unambiguous semidirect productD19⋊(C2×C32×C49)
unambiguous semidirect product(C19⋊C3)⋊(C22×C3×C49)
unambiguous semidirect product(C2×D19)⋊(C32×C49)
unambiguous semidirect product(C2×C19⋊C3)⋊(C2×C3×C49)
unambiguous semidirect product(C2×C3×D19)⋊(C3×C49)

Splittings

FittingC2×C3×C19×C49 ⋊ C2×C3
derived, SylowC19 ⋊ C22×C32×C49
HallC3×C49×C19⋊C3 ⋊ C22
HallC2×D19×C49 ⋊ C32
HallC19×C49 ⋊ C22×C32
HallC3×C19⋊C3 ⋊ C22×C49
HallC2×D19 ⋊ C32×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C49D19⋊C3
commutator, hypocenterC19C22×C32×C49
FrattiniC7C2×C3×C7×D19⋊C3
FittingC2×C3×C19×C49C2×C3
socleC2×C3×C7×C19C2×C3×C7
prime radicalC2×C3×C7×D19⋊C3C7
cosocleC7×C19C22×C32×C7
LCSG ▷ C19
UCSC1 ◁ C2×C3×C49

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5586

Conjugacy classes & character table

2646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 185);