Finite Group Databasebeta

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C₂×C₃⋊C₈×D₁₉ #14269249

order	1824
isoclinism	isoclinic class of D₃×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₃⋊C₈×D₁₉

Splittings

derived, Hall	C₃×C₁₉ ⋊ C₂²×C₈
Sylow	C₁₉ ⋊ C₂²×C₃⋊C₈
Sylow	C₃ ⋊ C₂×C₈×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂²×C₈
Frattini	C₄	C₂×D₃×D₁₉
Fitting	C₂×C₃×C₄×C₁₉	C₂²
socle	C₂²×C₃×C₁₉	C₂×C₄
prime radical	C₂²×C₃×D₁₉	C₄
cosocle	C₃×C₄×C₁₉	C₂³
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 912

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 476);