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C₃²×C₄²×C₆₁ #72187635

order	8784
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 276480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

abelian	C₃²×C₄²×C₆₁
multiplicative	(ℤ/9529)ˣ, (ℤ/19058)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₃²×C₆₁
socle, prime radical	C₂²×C₃²×C₆₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8784 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₈×C₆₁, C₂×C₃²×C₄²×C₆₁, C₃×C₄²×C₉×C₆₁, …
maximal normal subgroup of	C₃²×C₄×C₈×C₆₁, C₂×C₃²×C₄²×C₆₁, C₃×C₄²×C₉×C₆₁, …
maximal quotient of	C₃²×C₄×C₈×C₆₁, C₂×C₃²×C₄²×C₆₁, C₃×C₄²×C₉×C₆₁, …
automorphism group of	C₁₃×C₇₃₃
outer automorphism group of	C₁₃×C₇₃₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.