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C₂³×D₃×SD₁₆ #11708963

order	768
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂³×D₃×SD₁₆

Splittings

Fitting	C₂³×C₃×SD₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂⁴×SD₁₆

Subgroups

	subgroup	G/H
center	C₂⁴	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁶
Frattini	C₄	C₂⁵×D₃
Fitting	C₂³×C₃×SD₁₆	C₂
socle	C₂⁴×C₃	C₂×D₄
prime radical	C₂³×D₃×D₄	C₂
hypercenter	C₂³×SD₁₆	D₃
hypocenter	C₃	C₂⁴×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×SD₁₆

13310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂³×D₃×AGL(1,ℤ/8), C₂²×D₃×#450, D₃×#61050, …
maximal normal subgroup of	C₂³×D₃×AGL(1,ℤ/8), C₂²×D₃×#450, D₃×#61050, …
maximal quotient of	C₂²×D₃×#450

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083344);