Finite Group Databasebeta

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C3×#16812507 #23782861

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

Aliases

direct productC3×#16812507

Splittings

FittingC34×C43 ⋊ C3
SylowC43 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C43⋊C3)
commutator, cosocleC32×C43C33
FrattiniC32C32×C43⋊C3
FittingC34×C43C3
socleC32×C43H(3,𝔽3)
hypercenterC34C43⋊C3
hypocenterC43C3×AΣL(1,𝔽27)
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C34

252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1185 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#44533517, C9×#16812507, #44533541, …
maximal normal subgroup of#44533517, C9×#16812507, #44533541, …
maximal quotient ofC3×#23782686, C3×#23782688, C3×#23782689, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 245);