Finite Group Databasebeta

C3×C4×(C2×D9)⋊C4 #13142400

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×C4×(C2×D9)⋊C4

Splittings

FittingC2×C3×C42×C9 ⋊ C2
SylowC3×C9 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3×C4C2×D9
commutatorC2×C9C2×C3×C42
FrattiniC23×C3C22×C3×D3
FittingC2×C3×C42×C9C2
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
cosocleC23×C9C23×C3
hypercenterC2×C3×C42D9
hypocenterC9C3×C4×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42

882 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, 8463);