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C₂⁴×C₄×C₈₁ #72184558

order	5184
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 557383680
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₄×C₈₁
multiplicative	(ℤ/19560)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

3405 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	C₂⁴×C₈×C₈₁, C₂³×C₄²×C₈₁, C₂⁵×C₄×C₈₁, …
maximal normal subgroup of	C₂⁴×C₈×C₈₁, C₂³×C₄²×C₈₁, C₂⁵×C₄×C₈₁, …
maximal quotient of	C₂⁴×C₈×C₈₁, C₂³×C₄²×C₈₁, C₂⁵×C₄×C₈₁, …
automorphism group of	C₃×C₅×C₈×C₁₆₃
outer automorphism group of	C₃×C₅×C₈×C₁₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.