Finite Group Databasebeta

C9×#6308 #14518973

order1944
isoclinismisoclinic class of #6308
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C33

Aliases

direct productC9×#6308

Splittings

SylowC33×C9 ⋊ Q8

Subgroups

subgroupG/H
centerC2×C9C2×C3⋊(C3⋊D3)
commutatorC2×C33C22×C9
FrattiniC2×C3C2×C3×C3⋊(C3⋊D3)
FittingC33×C4×C9C2
socle, prime radical, cosocleC2×C34C22×C3
hypercenterC4×C9C3⋊(C3⋊D3)
hypocenterC33Q8×C9
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C9 ◁ C4×C9

972 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3367);