Finite Group Databasebeta

C2×C9×C3⋊(C3⋊Dic3) #14518994

order1944
isoclinismisoclinic class of C3⋊(C3⋊D3)
automorphism?
homologyAbelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2×C33

Aliases

direct productC2×C9×C3⋊(C3⋊Dic3)
unambiguous semidirect product(C2×C3)⋊(C9×C3⋊Dic3)

Splittings

derivedC33 ⋊ C2×C4×C9
SylowC33×C9 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C9C3⋊(C3⋊D3)
commutator, hypocenterC33C2×C4×C9
FrattiniC2×C3C2×C3×C3⋊(C3⋊D3)
FittingC22×C33×C9C2
socle, prime radicalC22×C34C2×C3
cosocleC2×C34C22×C3
LCSG ▷ C33
UCSC1 ◁ C22×C9

1452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3388);