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C₂×C₄×C₂₅×C₈₁ #72194169

order	16200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₄×C₂₅×C₈₁
multiplicative	(ℤ/16463)ˣ, (ℤ/20255)ˣ, (ℤ/20375)ˣ, (ℤ/24303)ˣ, (ℤ/24543)ˣ, (ℤ/30375)ˣ, (ℤ/32404)ˣ, (ℤ/32926)ˣ, (ℤ/40510)ˣ, (ℤ/40750)ˣ, (ℤ/48606)ˣ, (ℤ/49086)ˣ, (ℤ/60750)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅×C₂₇	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂×C₅×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₈×C₂₅×C₈₁, C₄²×C₂₅×C₈₁, C₂²×C₄×C₂₅×C₈₁
maximal normal subgroup of	C₂×C₈×C₂₅×C₈₁, C₄²×C₂₅×C₈₁, C₂²×C₄×C₂₅×C₈₁
maximal quotient of	C₂×C₈×C₂₅×C₈₁, C₄²×C₂₅×C₈₁, C₂²×C₄×C₂₅×C₈₁
automorphism group of	C₁₀₁×C₁₆₃, C₁₂₅×C₂₄₃
outer automorphism group of	C₁₀₁×C₁₆₃, C₁₂₅×C₂₄₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.