Finite Group Databasebeta

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C₂³×C₃×C₄×C₈×C₁₉ #72192736

order	14592
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3170893824
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian	C₂³×C₃×C₄×C₈×C₁₉
multiplicative	(ℤ/54840)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₃×C₁₉
socle, prime radical	C₂⁵×C₃×C₁₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

9276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14592 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄×C₁₆×C₁₉, C₂³×C₃×C₈²×C₁₉, C₂²×C₃×C₄²×C₈×C₁₉, …
maximal normal subgroup of	C₂³×C₃×C₄×C₁₆×C₁₉, C₂³×C₃×C₈²×C₁₉, C₂²×C₃×C₄²×C₈×C₁₉, …
maximal quotient of	C₂³×C₃×C₄×C₁₆×C₁₉, C₂³×C₃×C₈²×C₁₉, C₂²×C₃×C₄²×C₈×C₁₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.