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C₂×C₄²×C₅²×C₉ #72186272

order	7200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 4423680
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄×C₅

Aliases

abelian	C₂×C₄²×C₅²×C₉
multiplicative	(ℤ/9955)ˣ, (ℤ/10175)ˣ, (ℤ/13575)ˣ, (ℤ/18100)ˣ, (ℤ/19910)ˣ, (ℤ/20350)ˣ, (ℤ/27150)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂³×C₃×C₅²
socle, prime radical	C₂³×C₃×C₅²	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

1296 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₅²×C₈×C₉, C₄³×C₅²×C₉, C₂²×C₄²×C₅²×C₉, …
maximal normal subgroup of	C₂×C₄×C₅²×C₈×C₉, C₄³×C₅²×C₉, C₂²×C₄²×C₅²×C₉, …
maximal quotient of	C₂×C₄×C₅²×C₈×C₉, C₄³×C₅²×C₉, C₂²×C₄²×C₅²×C₉, …
automorphism group of	C₅×C₁₁×C₁₈₁, C₁₁×C₂₅×C₃₇
outer automorphism group of	C₅×C₁₁×C₁₈₁, C₁₁×C₂₅×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.