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C3×H(3,𝔽3)×C43⋊C3 #23782910

order10449
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C37

Aliases

direct productC3×H(3,𝔽3)×C43⋊C3

Splittings

FittingC3×H(3,𝔽3)×C43 ⋊ C3
SylowC43 ⋊ C32×H(3,𝔽3)

Subgroups

subgroupG/H
centerC32C32×C43⋊C3
commutator, cosocleC3×C43C34
FrattiniC3C33×C43⋊C3
FittingC3×H(3,𝔽3)×C43C3
socleC32×C43C33
hypercenterC3×H(3,𝔽3)C43⋊C3
hypocenterC43C32×H(3,𝔽3)
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC43⋊C3×#6856, C43⋊C3×#6857, C43⋊C3×#6859, …
maximal normal subgroup ofC43⋊C3×#6856, C43⋊C3×#6857, C43⋊C3×#6859, …
maximal quotient ofC3×C32⋊C9×C43⋊C3, C9×H(3,𝔽3)×C43⋊C3, C3×#23782783, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 294);