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#18081785

order	4864
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₈×C₄⋊C₄×C₁₉ ⋊ C₂
Sylow	C₁₉ ⋊ #9734

Subgroups

	subgroup	G/H
center	C₂³	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₈×C₄⋊C₄×C₁₉	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂×#11926921	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₈×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#9734
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₈×C₄⋊C₄

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2432

Polycyclic presentation:

2^8,19|a^2=f,b^2=dfgh,c^2=eg,d^2=gh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^18,d^b=dh,f^b=fh

Conjugacy classes & character table

778 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 68814);