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C₂×D₃×AGL(1,ℤ/16) #72219825

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×D₃×AGL(1,ℤ/16)

Splittings

Fitting	C₂×C₃×AGL(1,ℤ/16) ⋊ C₂
Sylow	C₃ ⋊ C₂²×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂²	D₃×#442
commutator	C₃×C₈	C₂⁴×C₄
Frattini	C₂×C₈	C₂⁴×D₃
Fitting	C₂×C₃×AGL(1,ℤ/16)	C₂
socle	C₂²×C₃	C₂×#442
prime radical	C₂×D₃×#509	C₂
cosocle	C₂×C₃×C₈	C₂⁵
hypercenter	C₂×AGL(1,ℤ/16)	D₃
hypocenter	C₃	C₂²×AGL(1,ℤ/16)
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ C₂×AGL(1,ℤ/16)

4268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃⋊D₃×AGL(1,ℤ/16), D₃²×AGL(1,ℤ/16), D₃×#495725, …
maximal normal subgroup of	D₃×#495725, D₃×#496124, D₃×#495850, …
maximal quotient of	C₂×C₃⋊D₃×AGL(1,ℤ/16), D₃²×AGL(1,ℤ/16), C₂×D₃×#12067, …
automorphism group of	#4506, #4904, D₃×D₁₆, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.