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C3×C4×D3×3−1+2 #14518888

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

Aliases

direct productC3×C4×D3×3−1+2
unambiguous semidirect product(C4×D3×C9)⋊C32

Splittings

FittingC32×C4×3−1+2 ⋊ C2
SylowC32×3−1+2 ⋊ C2×C4

Subgroups

subgroupG/H
centerC32×C4C32×D3
commutatorC32C2×C33×C4
FrattiniC2×C3C2×C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C22×C32
prime radicalC2×C33×D3C2×C3
cosocleC2×C32C22×C33
hypercenterC3×C4×3−1+2D3
hypocenterC3C2×C3×C4×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C32×C4 ◁ C3×C4×3−1+2

926 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, 3282);