Finite Group Databasebeta

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C₂×C₃²×C₄³×C₉ #72189028

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 128421199872
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃³×C₄³

Aliases

abelian	C₂×C₃²×C₄³×C₉
multiplicative	(ℤ/16835)ˣ, (ℤ/21645)ˣ, (ℤ/33670)ˣ, (ℤ/43290)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃³
socle, prime radical	C₂⁴×C₃³	C₂³×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

31800 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄²×C₈×C₉, C₃²×C₄⁴×C₉, C₂²×C₃²×C₄³×C₉, …
maximal normal subgroup of	C₂×C₃²×C₄²×C₈×C₉, C₃²×C₄⁴×C₉, C₂²×C₃²×C₄³×C₉, …
maximal quotient of	C₂×C₃²×C₄²×C₈×C₉, C₃²×C₄⁴×C₉, C₂²×C₃²×C₄³×C₉, …
automorphism group of	C₅×C₇×C₁₃×C₃₇
outer automorphism group of	C₅×C₇×C₁₃×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.