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C3×#16812508 #23782862

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

Aliases

direct productC3×#16812508

Splittings

FittingC3×3−1+2×C43 ⋊ C3
SylowC43 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C43⋊C3)
commutator, cosocleC32×C43C33
FrattiniC32C32×C43⋊C3
FittingC3×3−1+2×C43C3
socleC32×C43H(3,𝔽3)
hypercenterC3×3−1+2C43⋊C3
hypocenterC43C3×AΣL(1,𝔽27)
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44533519, C9×#16812508, #44533544, …
maximal normal subgroup of#44533519, C9×#16812508, #44533544, …
maximal quotient ofC3×#23782687, C3×#23782688, C3×#23782690, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 246);