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C₂⁴×C₅×C₉×C₁₉ #72191891

order	13680
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8709120
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂⁴×C₅×C₉×C₁₉
multiplicative	(ℤ/29032)ˣ, (ℤ/31768)ˣ, (ℤ/41256)ˣ, (ℤ/43548)ˣ, (ℤ/47652)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁴×C₃×C₅×C₁₉
socle, prime radical	C₂⁴×C₃×C₅×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₅×C₉×C₁₉, C₂⁵×C₅×C₉×C₁₉
maximal normal subgroup of	C₂³×C₄×C₅×C₉×C₁₉, C₂⁵×C₅×C₉×C₁₉
maximal quotient of	C₂³×C₄×C₅×C₉×C₁₉, C₂⁵×C₅×C₉×C₁₉
automorphism group of	C₈×C₁₉×C₁₉₁, C₈×C₁₁×C₃₆₁
outer automorphism group of	C₈×C₁₉×C₁₉₁, C₈×C₁₁×C₃₆₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.