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C₃²×C₄²×C₇₁ #72188846

order	10224
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 322560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

abelian	C₃²×C₄²×C₇₁
multiplicative	(ℤ/11089)ˣ, (ℤ/22178)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₇₁
socle, prime radical	C₂²×C₃²×C₇₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10224 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₈×C₇₁, C₂×C₃²×C₄²×C₇₁, C₃×C₄²×C₉×C₇₁, …
maximal normal subgroup of	C₃²×C₄×C₈×C₇₁, C₂×C₃²×C₄²×C₇₁, C₃×C₄²×C₉×C₇₁, …
maximal quotient of	C₃²×C₄×C₈×C₇₁, C₂×C₃²×C₄²×C₇₁, C₃×C₄²×C₉×C₇₁, …
automorphism group of	C₁₃×C₈₅₃
outer automorphism group of	C₁₃×C₈₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.