Finite Group Databasebeta

C3×C4⋊(C9⋊D9) #14517489

order1944
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C9

Aliases

direct productC3×C4⋊(C9⋊D9)
unambiguous semidirect productC4⋊(C3×C9⋊D9)

Splittings

FittingC3×C4×C92 ⋊ C2
SylowC3×C92 ⋊ D4

Subgroups

subgroupG/H
centerC2×C3C2×C9⋊D9
commutator, cosocleC2×C92C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC3×C4×C92C2
socleC2×C33C2×C3⋊D3
hypercenterC3×C4C9⋊D9
hypocenterC92C3×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2×C3 ◁ C3×C4

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1883);