Finite Group Databasebeta

← Prev (#18072407) Next (#18072409) →

#18072408

order	4864
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Splittings

C₁₉ ⋊ #7978

Subgroups

	subgroup	G/H
center	C₂²	C₂×C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#432	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#432	D₁₉
hypocenter	C₁₉	#7978
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#432

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1216

Polycyclic presentation:

2^8,19|a^2=e,b^2=f,c^2=gh,d^2=gh,f^2=h,b^a=bd,d^a=dg,f^a=fgh,i^a=i^18,c^b=cg,e^b=eh,i^b=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, 59437);