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3−1+2⋊(C43⋊C9) #23782723

order10449
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect product3−1+2⋊(C43⋊C9)

Splittings

SylowC43 ⋊ 3−1+2⋊C9

Subgroups

subgroupG/H
centerC32C32⋊(C43⋊C3)
commutatorC32×C43C3×C9
FrattiniC33C3×C43⋊C3
FittingC3×3−1+2×C43C3
socleC32×C43H(3,𝔽3)
prime radical, cosocleC33×C43C32
hypercenterC3×3−1+2C43⋊C3
hypocenterC433−1+2⋊C9
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^5,43|a^3=d,b^3=e,b^a=bc,c^a=ce,f^a=f^36,c^b=ce

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC43⋊C3×3−1+2⋊C9, C3×3−1+2⋊(C43⋊C9), #44533419, …
maximal normal subgroup ofC43⋊C3×3−1+2⋊C9, C3×3−1+2⋊(C43⋊C9), #44533419, …
maximal quotient of3−1+2⋊(C43⋊C27), #44531903, #44531906, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 107);