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C₂³×C₈×C₉×C₁₆ #72187994

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8455716864
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₈

Aliases

abelian	C₂³×C₈×C₉×C₁₆
multiplicative	(ℤ/29784)ˣ, (ℤ/31008)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₈	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₃×C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

18015 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₈×C₉×C₃₂, C₂³×C₉×C₁₆², C₂²×C₄×C₈×C₉×C₁₆, …
maximal normal subgroup of	C₂³×C₈×C₉×C₃₂, C₂³×C₉×C₁₆², C₂²×C₄×C₈×C₉×C₁₆, …
maximal quotient of	C₂³×C₈×C₉×C₃₂, C₂³×C₉×C₁₆², C₂²×C₄×C₈×C₉×C₁₆, …
automorphism group of	C₃×C₈×C₁₇×C₇₃, C₃×C₁₇×C₁₉×C₃₂
outer automorphism group of	C₃×C₈×C₁₇×C₇₃, C₃×C₁₇×C₁₉×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.