Finite Group Databasebeta

C22×C3×(C2×D9)⋊C4 #13153537

order1728
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C3×(C2×D9)⋊C4

Splittings

FittingC23×C3×C4×C9 ⋊ C2
SylowC3×C9 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24×C3C2×D9
commutatorC2×C9C23×C3×C4
FrattiniC22×C3C23×C3×D3
FittingC23×C3×C4×C9C2
socleC24×C32C2×D3
prime radicalC24×C3×D9C2
cosocleC22×C9C24×C3
hypercenterC23×C3×C4D9
hypocenterC9C22×C3×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C24×C3 ◁ C23×C3×C4

2258 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, 19600);