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C₂⁴×C₃²×C₄×C₁₉ #72189498

order	10944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8918138880
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁴×C₃²×C₄×C₁₉
multiplicative	(ℤ/38472)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₃²×C₁₉
socle, prime radical	C₂⁵×C₃²×C₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

8172 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	C₂⁴×C₃²×C₈×C₁₉, C₂³×C₃²×C₄²×C₁₉, C₂⁵×C₃²×C₄×C₁₉
maximal normal subgroup of	C₂⁴×C₃²×C₈×C₁₉, C₂³×C₃²×C₄²×C₁₉, C₂⁵×C₃²×C₄×C₁₉
maximal quotient of	C₂⁴×C₃²×C₈×C₁₉, C₂³×C₃²×C₄²×C₁₉, C₂⁵×C₃²×C₄×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.