Finite Group Databasebeta

C2×C3×#63364 #13142378

order1728
isoclinismisoclinic class of Dic36
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#63364

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#104

Subgroups

subgroupG/H
centerC2×C3×C4D36
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C42×C9C2
socleC22×C32(C2×D3)⋊C4
prime radicalC2×C3×#3697C2
cosocleC2×C4×C9C23×C3
hypercenterC2×C3×C42D9
hypocenterC9C2×C3×#104
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×C42

618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8441);