Finite Group Databasebeta

C3×#20258262 #31825604

order18063
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32

Aliases

direct productC3×#20258262

Splittings

SylowC223 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC32C3×C223⋊C3
commutator, cosocleC3×C223C33
FrattiniC3C32×C223⋊C3
Fitting, prime radicalC33×C223C3
socleC32×C223C32
hypercenterC33C223⋊C3
hypocenterC223C3×3−1+2
LCSG ▷ C3×C223 ▷ C223
UCSC1 ◁ C32 ◁ C33

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6021

Conjugacy classes & character table

2031 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18063, 45);