Finite Group Databasebeta

C2×C3×D3×#208 #13174408

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×D3×#208

Splittings

SylowC33 ⋊ C22×M16

Subgroups

subgroupG/H
centerC2×C3×C4C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22×C4
prime radicalC23×C32×D3C4
cosocleC32×C4C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C22×C3×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

1618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 40471);