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C3×#16812506 #23782860

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

Aliases

direct productC3×#16812506

Splittings

FittingC3×H(3,𝔽3)×C43 ⋊ C3
SylowC43 ⋊ C3×AΣL(1,𝔽27)

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×AΣL(1,𝔽27)
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#16812506, #44533522, #44533543, …
maximal normal subgroup ofC9×#16812506, #44533522, #44533543, …
maximal quotient ofC3×#23782686, C3×#23782689, C3×#23782690, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 244);