Finite Group Databasebeta

C3×C4×#3697 #13152282

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×C4×#3697

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ C4×#41

Subgroups

subgroupG/H
centerC3×C42C2×D9
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC2×C3×C42×C9C2
socleC22×C32C23×D3
prime radicalC2×C3×#3697C2
cosocleC22×C9C24×C3
hypercenterC2×C3×C42D9
hypocenterC9C3×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C3×C42 ◁ C2×C3×C42

1038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18345);