Finite Group Databasebeta

C3×C4×#3663 #13141413

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×C4×#3663

Splittings

FittingC3×C4×C8×C9 ⋊ C2
SylowC3×C9 ⋊ C4×M16

Subgroups

subgroupG/H
centerC3×C42C2×D9
commutatorC2×C9C2×C3×C42
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C4×C8×C9C2
socleC22×C32C2×C4×D3
prime radicalC22×C3×D9C2×C4
cosocleC2×C4×C9C23×C3
hypercenterC3×C4×C8D9
hypocenterC9C3×C4×M16
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C3×C42 ◁ C3×C4×C8

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 7476);