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C₃×C₄²×C₅²×C₉ #72189347

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4976640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄×C₅

Aliases

abelian	C₃×C₄²×C₅²×C₉
multiplicative	(ℤ/11041)ˣ, (ℤ/22082)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃²×C₅²
socle, prime radical	C₂²×C₃²×C₅²	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

1200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄×C₅²×C₈×C₉, C₂×C₃×C₄²×C₅²×C₉, C₃×C₄²×C₅²×C₂₇, …
maximal normal subgroup of	C₃×C₄×C₅²×C₈×C₉, C₂×C₃×C₄²×C₅²×C₉, C₃×C₄²×C₅²×C₂₇, …
maximal quotient of	C₃×C₄×C₅²×C₈×C₉, C₂×C₃×C₄²×C₅²×C₉, C₃×C₄²×C₅²×C₂₇, …
automorphism group of	C₆₁×C₁₈₁
outer automorphism group of	C₆₁×C₁₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.