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C₂³×C₈×C₈₁ #72184543

order	5184
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2322432
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₈×C₈₁
multiplicative	(ℤ/15648)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₂₇	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₄×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

845 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₁₆×C₈₁, C₂²×C₄×C₈×C₈₁, C₂⁴×C₈×C₈₁, …
maximal normal subgroup of	C₂³×C₁₆×C₈₁, C₂²×C₄×C₈×C₈₁, C₂⁴×C₈×C₈₁, …
maximal quotient of	C₂³×C₁₆×C₈₁, C₂²×C₄×C₈×C₈₁, C₂⁴×C₈×C₈₁, …
automorphism group of	C₃×C₃₂×C₁₆₃
outer automorphism group of	C₃×C₃₂×C₁₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.