Finite Group Databasebeta

← Prev (#23782867) Next (#23782869) →

C3×#16812512 #23782868

order10449
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C34

Aliases

direct productC3×#16812512

Splittings

FittingC3×H(3,𝔽3)×C43 ⋊ C3
SylowC43 ⋊ C3×#732

Subgroups

subgroupG/H
centerC32C32⋊(C43⋊C3)
commutator, cosocleC32×C43C33
FrattiniC32C32×C43⋊C3
FittingC3×H(3,𝔽3)×C43C3
socleC32×C43H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C43⋊C3
hypocenterC43C3×#732
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#16812512, #44533533, #44533565, …
maximal normal subgroup ofC9×#16812512, #44533533, #44533565, …
maximal quotient ofC3×#23782686, C3×#23782687, C3×#23782695, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 252);