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C₂²×C₄×C₅×C₁₉₁ #72193291

order	15280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 145920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₅×C₁₉₁
multiplicative	(ℤ/21065)ˣ, (ℤ/28725)ˣ, (ℤ/30568)ˣ, (ℤ/38300)ˣ, (ℤ/42130)ˣ, (ℤ/45852)ˣ, (ℤ/57450)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅×C₁₉₁
socle, prime radical	C₂³×C₅×C₁₉₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₅×C₈×C₁₉₁, C₂×C₄²×C₅×C₁₉₁, C₂³×C₄×C₅×C₁₉₁
maximal normal subgroup of	C₂²×C₅×C₈×C₁₉₁, C₂×C₄²×C₅×C₁₉₁, C₂³×C₄×C₅×C₁₉₁
maximal quotient of	C₂²×C₅×C₈×C₁₉₁, C₂×C₄²×C₅×C₁₉₁, C₂³×C₄×C₅×C₁₉₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.