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C₂×C₃×C₈×C₉×C₁₆ #72185993

order	6912
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3538944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₈

Aliases

abelian	C₂×C₃×C₈×C₉×C₁₆
multiplicative	(ℤ/8687)ˣ, (ℤ/11169)ˣ, (ℤ/17374)ˣ, (ℤ/22338)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₈	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₃×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1990 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₃₂, C₂×C₃×C₉×C₁₆², C₃×C₄×C₈×C₉×C₁₆, …
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₃₂, C₂×C₃×C₉×C₁₆², C₃×C₄×C₈×C₉×C₁₆, …
maximal quotient of	C₂×C₃×C₈×C₉×C₃₂, C₂×C₃×C₉×C₁₆², C₃×C₄×C₈×C₉×C₁₆, …
automorphism group of	C₇×C₁₇×C₇₃, C₉×C₁₇×C₇₃
outer automorphism group of	C₇×C₁₇×C₇₃, C₉×C₁₇×C₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.