Finite Group Databasebeta

D3×#63818 #13170488

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

Aliases

direct productD3×#63818

Splittings

SylowC33 ⋊ C22×M16

Subgroups

subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C4
cosocleC33×C4C24
hypercenterC2×C4D33
hypocenterC33C22×M16
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

1618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#10595100, D3×#10590393, D3×#10591503
maximal normal subgroup ofD3×#10595100, D3×#10590393, D3×#10591503

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 36551);