Finite Group Databasebeta

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C₂×D₃×C₈×C₁₉ #14269651

order	1824
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₃×C₈×C₁₉

Splittings

Fitting	C₂×C₃×C₈×C₁₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂²×C₈×C₁₉
Hall	C₃×C₁₉ ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈×C₁₉	D₃
commutator, hypocenter	C₃	C₂²×C₈×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₈×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂×C₄
prime radical	C₂²×D₃×C₁₉	C₄
cosocle	C₃×C₄	C₂³×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₈×C₁₉

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 912

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 878);