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C₂²×C₄×C₈×C₈₁ #72189015

order	10368
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10616832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄×C₈×C₈₁
multiplicative	(ℤ/26080)ˣ, (ℤ/38880)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₂₇	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂×C₄×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

1900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₁₆×C₈₁, C₂²×C₈²×C₈₁, C₂×C₄²×C₈×C₈₁, …
maximal normal subgroup of	C₂²×C₄×C₁₆×C₈₁, C₂²×C₈²×C₈₁, C₂×C₄²×C₈×C₈₁, …
maximal quotient of	C₂²×C₄×C₁₆×C₈₁, C₂²×C₈²×C₈₁, C₂×C₄²×C₈×C₈₁, …
automorphism group of	C₅×C₃₂×C₁₆₃
outer automorphism group of	C₅×C₃₂×C₁₆₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.