Finite Group Databasebeta

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C2×C3×Dic3×3−1+2 #14518902

order1944
automorphism?
homologyAbelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×C3×Dic3×3−1+2
unambiguous semidirect product(C2×C3)⋊(C3×C4×3−1+2)
unambiguous semidirect product(C2×C9×Dic3)⋊C32

Splittings

SylowC32×3−1+2 ⋊ C2×C4

Subgroups

subgroupG/H
centerC22×C32C32×D3
commutatorC32C2×C33×C4
FrattiniC2×C3C2×C33×D3
FittingC22×C32×3−1+2C2
socleC22×C33C2×C32
prime radicalC22×C34C2×C3
cosocleC2×C32C22×C33
hypercenterC22×C3×3−1+2D3
hypocenterC3C2×C3×C4×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C22×C32 ◁ C22×C3×3−1+2

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3296);