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C₂³×D₃×AGL(1,ℤ/8) #72246584

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²⁰

Aliases

C₂³×D₃×AGL(1,ℤ/8)

Splittings

Fitting	C₂³×C₃×AGL(1,ℤ/8) ⋊ C₂
Sylow	C₃ ⋊ C₂⁴×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁷
Frattini	C₄	C₂⁶×D₃
Fitting	C₂³×C₃×AGL(1,ℤ/8)	C₂
socle	C₂⁴×C₃	C₂²×D₄
hypercenter	C₂³×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₂⁴×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×AGL(1,ℤ/8)

140036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂²×D₃×#3003, D₃×#359472, D₃×#394040, …
maximal normal subgroup of	C₂²×D₃×#3003, D₃×#359472, D₃×#394040, …
maximal quotient of	C₂²×D₃×#3003

GAP

Past the SmallGroups library coverage — no SmallGroups id.