Finite Group Databasebeta

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C₂×C₁₉×#215 #14269695

order	1824
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₁₉×#215

Splittings

Fitting	C₂×C₃×Q₈×C₁₉ ⋊ C₂
Hall	C₃×C₁₉ ⋊ C₂×SD₁₆
Sylow	C₃ ⋊ C₂×SD₁₆×C₁₉

Subgroups

	subgroup	G/H
center	C₂²×C₁₉	#67
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	D₄
prime radical	C₂×C₁₉×D₁₂	C₂
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₂×SD₁₆×C₁₉
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×Q₈×C₁₉

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 912

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 922);