Finite Group Databasebeta

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C2×C3×D349⋊C3 #27160267

order12564
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D349⋊C3
unambiguous semidirect productD349⋊(C2×C32)
unambiguous semidirect product(C349⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D349)⋊C32
unambiguous semidirect product(C2×C349⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D349)⋊C3

Splittings

Fitting, socleC2×C3×C349 ⋊ C2×C3
derived, SylowC349 ⋊ C22×C32
HallC3×C349⋊C3 ⋊ C22
HallC2×D349 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D349⋊C3
commutator, cosocle, hypocenterC349C22×C32
FrattiniC1G
Fitting, socleC2×C3×C349C2×C3
LCSG ▷ C349
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12564, 34);