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#18078030

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

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₁₉×Q₈⋊C₈ ⋊ C₂
Sylow	C₁₉ ⋊ #9098

Subgroups

	subgroup	G/H
center	C₂×C₄	#10597384
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#64541	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#9098
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2432

Polycyclic presentation:

2^8,19|a^2=f,b^2=dfg,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^18,c^b=ch,d^b=dg,e^b=eg,f^b=fg,i^b=i^18,d^c=dg,e^c=eg,f^c=fg,i^c=i^18

Conjugacy classes & character table

556 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 65059);