Finite Group Databasebeta

C2×C3×#63380 #13143096

order1728
isoclinismisoclinic class of Dic36
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×#63380

Splittings

FittingC22×C3×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23×C3D36
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC22×C3×C8×C9C2
socleC23×C32D12
prime radicalC22×C3×D36C2
cosocleC2×C4×C9C23×C3
hypercenterC22×C3×C8D9
hypocenterC9C2×C3×#102
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×C8

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 9159);