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C₂²×C₄²×C₅×C₁₉ #72185264

order	6080
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10616832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄²×C₅×C₁₉
multiplicative	(ℤ/15280)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₅×C₁₉
socle, prime radical	C₂⁴×C₅×C₁₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₂³×C₄²×C₅×C₁₉, …
maximal normal subgroup of	C₂²×C₄×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₂³×C₄²×C₅×C₁₉, …
maximal quotient of	C₂²×C₄×C₅×C₈×C₁₉, C₂×C₄³×C₅×C₁₉, C₂³×C₄²×C₅×C₁₉, …
automorphism group of	C₅×C₁₆×C₁₉₁
outer automorphism group of	C₅×C₁₆×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.