Finite Group Databasebeta

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C₂×C₁₉⋊#1308 #18072940

order	4864
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₁₉⋊#1308
unambiguous semidirect product	(C₂×C₁₉)⋊#1308

Splittings

C₁₉ ⋊ C₂×#1308

Subgroups

	subgroup	G/H
center	C₂³	C₁₉⋊#95
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#432	C₂
socle	C₂³×C₁₉	#95
prime radical	C₂⁴×C₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#432	D₁₉
hypocenter	C₁₉	C₂×#1308
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#432

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59969);