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C₂³×C₈×C₉×C₁₉ #72189491

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4644864
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₈×C₉×C₁₉
multiplicative	(ℤ/34656)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂⁴×C₃×C₁₉
socle, prime radical	C₂⁴×C₃×C₁₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1014 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10944 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₉×C₁₆×C₁₉, C₂²×C₄×C₈×C₉×C₁₉, C₂⁴×C₈×C₉×C₁₉
maximal normal subgroup of	C₂³×C₉×C₁₆×C₁₉, C₂²×C₄×C₈×C₉×C₁₉, C₂⁴×C₈×C₉×C₁₉
maximal quotient of	C₂³×C₉×C₁₆×C₁₉, C₂²×C₄×C₈×C₉×C₁₉, C₂⁴×C₈×C₉×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.