Finite Group Databasebeta

← Prev (#23782865) Next (#23782867) →

C3×#16812511 #23782866

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

Aliases

direct productC3×#16812511

Splittings

FittingC3×3−1+2×C43 ⋊ C3
SylowC43 ⋊ C3×#731

Subgroups

subgroupG/H
centerC32C32⋊(C43⋊C3)
commutator, cosocleC32×C43C33
FrattiniC32C32×C43⋊C3
FittingC3×3−1+2×C43C3
socleC32×C43H(3,𝔽3)
prime radicalC3×C32⋊(C43⋊C3)C3
hypercenterC3×3−1+2C43⋊C3
hypocenterC43C3×#731
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44533526, C9×#16812511, #44533555, …
maximal normal subgroup of#44533526, C9×#16812511, #44533555, …
maximal quotient ofC3×#23782688, C3×#23782691, C3×#23782692, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 250);